English
Hindi

Question

Download Solution PDF

If  , then evaluate 

This question was previously asked in
RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 1)
Download PDF Attempt in App
View all RRB NTPC Papers >

Answer (Detailed Solution Below)

Option 1 :
Free Tests
View all Free tests >
Free
RRB NTPC Graduate Level Full Test - 01
100 Qs. 100 Marks 90 Mins
Start Now

Detailed Solution

Download Solution PDF
<p><strong>Given:</strong></p><p><amp-mathml inline data-formula="\(\tan\theta = \frac{7}{8}\)"></amp-mathml></p><p>Expression to evaluate: <amp-mathml inline data-formula="\(\dfrac{(1 + \sin\theta)(1 - \sin\theta)}{(1 + \cos\theta)(1 - \cos\theta)(\cot\theta)}\)"></amp-mathml></p><p><strong>Formula used:</strong></p><p>1. (a + b)(a - b) = a<sup>2</sup> - b<sup>2</sup></p><p>2. <amp-mathml inline data-formula="\(\sin^2\theta + \cos^2\theta = 1\)"></amp-mathml></p><p>⇒ <amp-mathml inline data-formula="\(1 - \sin^2\theta = \cos^2\theta\)"></amp-mathml></p><p>⇒ <amp-mathml inline data-formula="\(1 - \cos^2\theta = \sin^2\theta\)"></amp-mathml></p><p>3. <amp-mathml inline data-formula="\(\cot\theta = \dfrac{\cos\theta}{\sin\theta}\)"></amp-mathml></p><p>4. <amp-mathml inline data-formula="\(\cot\theta = \dfrac{1}{\tan\theta}\)"></amp-mathml></p><p><strong>Calculations:</strong></p><p>Simplify the numerator:</p><p>Numerator = <amp-mathml inline data-formula="\((1 + \sin\theta)(1 - \sin\theta)\)"></amp-mathml></p><p>⇒ Numerator = <amp-mathml inline data-formula="\(1^2 - \sin^2\theta\)"></amp-mathml></p><p>⇒ Numerator = <amp-mathml inline data-formula="\(1 - \sin^2\theta\)"></amp-mathml></p><p>⇒ Numerator = <amp-mathml inline data-formula="\(\cos^2\theta\)"></amp-mathml></p><p>Simplify the denominator:</p><p>Denominator = <amp-mathml inline data-formula="\((1 + \cos\theta)(1 - \cos\theta)(\cot\theta)\)"></amp-mathml></p><p>⇒ Denominator = <amp-mathml inline data-formula="\((1^2 - \cos^2\theta)(\cot\theta)\)"></amp-mathml></p><p>⇒ Denominator = <amp-mathml inline data-formula="\((1 - \cos^2\theta)(\cot\theta)\)"></amp-mathml></p><p>⇒ Denominator = <amp-mathml inline data-formula="\(\sin^2\theta \times \cot\theta\)"></amp-mathml></p><p>Substitute <amp-mathml inline data-formula="\(\cot\theta = \dfrac{\cos\theta}{\sin\theta}\)"></amp-mathml>:</p><p>⇒ Denominator = <amp-mathml inline data-formula="\(\sin^2\theta \times \dfrac{\cos\theta}{\sin\theta}\)"></amp-mathml></p><p>⇒ Denominator = <amp-mathml inline data-formula="\(\sin\theta \cos\theta\)"></amp-mathml></p><p>Now, substitute the simplified numerator and denominator into the expression:</p><p>Expression = <amp-mathml inline data-formula="\(\dfrac{\cos^2\theta}{\sin\theta \cos\theta}\)"></amp-mathml></p><p>Cancel out  <amp-mathml inline data-formula="\(\cos\theta\)"></amp-mathml> from numerator and denominator:</p><p>⇒ Expression = <amp-mathml inline data-formula="\(\dfrac{\cos\theta}{\sin\theta}\)"></amp-mathml></p><p>⇒ Expression = <amp-mathml inline data-formula="\(\cot\theta\)"></amp-mathml></p><p>Given <amp-mathml inline data-formula="\(\tan\theta = \dfrac{7}{8}\)"></amp-mathml>.</p><p>Since <amp-mathml inline data-formula="\(\cot\theta = \dfrac{1}{\tan\theta}\)"></amp-mathml>:</p><p>⇒ Expression = <amp-mathml inline data-formula="\(\dfrac{1}{\frac{7}{8}}\)"></amp-mathml></p><p>⇒ Expression = <amp-mathml inline data-formula="\(\dfrac{8}{7}\)"></amp-mathml></p><p><strong>∴ The value of the expression is <amp-mathml inline data-formula="\(\dfrac{8}{7}\)"></amp-mathml>.</strong></p> - www.bijoux-oeil-de-tigre.com
Download Solution PDF
Latest RRB NTPC Updates

Last updated on Jul 19, 2025

-> RRB NTPC Under Graduate Exam Date 2025 has been released on the official website of the Railway Recruitment Board.

-> The RRB NTPC Admit Card will be released on its official website for RRB NTPC Under Graduate Exam 2025.

-> CSIR NET City Intimation Slip 2025 Out @csirnet.nta.ac.in

-> HSSC CET Admit Card 2025 has been released @hssc.gov.in

-> Candidates who will appear for the RRB NTPC Exam can check their RRB NTPC Time Table 2025 from here. 

-> The RRB NTPC 2025 Notification released for a total of 11558 vacancies. A total of 3445 Vacancies have been announced for Undergraduate posts like Commercial Cum Ticket Clerk, Accounts Clerk Cum Typist, Junior Clerk cum Typist & Trains Clerk.

-> A total of 8114 vacancies are announced for Graduate-level posts in the Non-Technical Popular Categories (NTPC) such as Junior Clerk cum Typist, Accounts Clerk cum Typist, Station Master, etc.

-> Prepare for the exam using RRB NTPC Previous Year Papers.

-> Get detailed subject-wise UGC NET Exam Analysis 2025 and UGC NET Question Paper 2025 for shift 1 (25 June) here

->Bihar Police Driver Vacancy 2025 has been released @csbc.bihar.gov.in.

‹‹ Previous Ques
Next Ques ››
Exams Tests Super Practice

More Trigonometry Questions

Q1.A ladder is resting on the ground with the top end in contact with the top of a wall of a height of 12 metres. If the length of the ladder is 13 metres, at what distance from the wall is the base of the ladder on the ground?
Q2.Cos0°. Cos1°. Cos2°, Cos3° ......... Cos90° =? 
Q3.If sin 2A = 2 sin A, then A = ?
Q4.If Sin \(A=\frac{3}{5}\) then find value of Cos A? 
Q5.Sin π = ?
Q6.Cosec2θ - Cot2θ = ?
Q7.If cot θ + cosecθ = 5, θ being an acute angle, then the value of 13 cos θ is:
Q8.An aeroplane at an altitude of 3000 m observes the angles of depression of opposite points on the two banks of a river to be 45 and 60 respectively. Find the width of the river in metre. 
Q9.An aeroplane at an altitude of 3000 m observes the angles of depression of opposite points on the two banks of a river to be 45 and 60 respectively. Find the width of the river in metre.
Q10.1 + sec2 46° - cot2 44° =
Suggested Test Series
View All >
RRB NTPC Mock Test Series 2024-25 (CBT 1 + CBT 2)
2341 Total Tests with 3 Free Tests
Start Free Test
Current Affairs (CA) 2025 Mega Pack for SSC/Railways/State Exam Mock Test
431 Total Tests with   1 Free Tests
Start Free Test

More Quantitative Aptitude Questions

Q1.Perimeter of a rectangular field is equal to the perimeter of a triangular field whose sides are in the ratio 3:2:4 respectively. lf area of rectangular field is 500 m2 and sides are in the ratio 5:4 respectively, then calculate the longer side of the triangular field.
Q2.A cistern has an inlet pipe and an outlet pipe. Inlet pipe can fill three-fourth of the cistern in 24 minutes while outlet pipe can empty the one-third filled cistern in 16 minutes. If both the pipes are opened together, then the cistern will be completely filled in-
Q3.In a family, three sons were born for every 3 years one after the other. If the ratio of present ages of father and the eldest son is 15:7 and the average of the present ages of the 3 sons is 18 years. What will be the ratio of the ages of the father and the youngest son after 5 years?
Q4.Train A of length 80m while moving crosses a pole in 16 seconds. lf it is known that the lengths of train B and train A is in the ratio of 3:1, then how long would it take train B to cross a platform which is half the length of train A if the speed of train B is same as that of train A?
Q5.Can A and Can B contain a mixture of soda and water in the ratio of 5 : 3 and 7 : 2 respectively If soda and water are taken out in the ratio of P : Q from can A and B respectively to form a new mixture in which the ratio of soda and water is 12 : 5 respectively, then find the value Of P:Q?
Q6.A boat can covers a certain distance in upstream and same distance in downstream in total of 7 hours 48 minutes, If upstream speed of the boat is 62.5%. of downstream speed of the boat and speed of the stream is 3 km/h, what is the total distance covered by the boat?
Q7.M and R went for shopping and bought two sarees each at different cost. Cost price of saree bought by R is Rs.250 more than the cost price of saree bought by M. Shopkeeper earned a profit of 20% on selling both the sarees together to R and M which he bought them at total Rs.6000. At what cost did M buy saree?
Q8.There are three numbers m, n, and p, such that sum of m and n is 144, sum of thrice of n and five times of p is 464, and sum of p and m is 160, then what is the value of p?
Q9.While calculating average marks of 60 students, the two digits of original marks of a student are written reversed and thereby average of marks is increased by 0.6 Find the difference between the two digits of marks of the student?  
Q10.Simple interest received on a certain sum at a rate of simple interest of 5% for 2 years is Rs.780. If the rate of interest remains same, what will be the total amount at the time of withdrawal at the end of 5 years.  
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti master online teen patti 3a teen patti go teen patti boss