If where is an acute angle, then what is the value of

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 09 Dec 2022 Shift 3)

Answer 1

Given:

, where θ is an acute angle

Formula Used:

sin²θ + cos²θ = 1

tan θ = , and

cot θ =

Calculation:

In order to find and , we need :

sin2θ + cos2θ = 1

cos θ =

⇒

Now, calculating :

⇒

∴ The value of tan θ + cot θ is .

Shortcut Trick

= P/H, we know the Pythagorean triplet (8, 15, 17)

Then, base (B) = 15, so tan θ = P/B = 8/15, cot θ = 15/17

⇒ tan θ + cot θ

⇒ 8/15 + 15/8

⇒