Question
Download Solution PDFFind the value of sec 33° cosec 57°- cot 57° tan 33° + cot 47° cot 43°
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
- \(sec 33° cosec 57°- cot 57° tan 33° + cot 47° cot 43°\)
Formula used:
- \(cosec\:\theta= sec\:(90-\theta)\)
- \(cot\:\theta= tan\:(90-\theta)\)
- \(cot\:\theta\:tan\:\theta=1\)
- \(sec^2\theta-tan^2\theta=1\)
Calculations:
We know that,
- \(cosec\:57^\circ= sec\:(90-57)^\circ=sec33^\circ\)
- \(cot\:57^\circ= tan\:(90-57)^\circ=tan33^\circ\)
- \(cot\:47^\circ= tan\:(90-47)^\circ=tan43^\circ\)
Now, according to the question,
\(sec 33° cosec 57°- cot 57° tan 33° + cot 47° cot 43°\\ =sec 33° sec 33° - tan 33° tan 33° + tan43°cot 43°\\ =sec^2 33°-tan^2 33°+1\\ =1+1\\ =2\)
Therefore, the correct answer is option 4.
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