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Question and Answer

The value of \( sin\theta .cos\theta (tan\theta +cot\theta )\) is
(A) 1
(B) 2
(C) -1
(D) 0

Answer

(A)
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Solution

\( sin\theta\;cos\theta (tan\theta +cot\theta ) \)
\( sin\theta\;cos\theta\;tan\theta +sin\theta\;cos\theta\;cot\theta \)
\( sin\theta\;cos\theta \frac{sin\theta }{cos\theta }+sin\theta\;cos\theta \frac{cos\theta }{sin\theta }\)
\( si{n}^{2}\theta +co{s}^{2}\theta =1,  (\therefore\;si{n}^{2}\theta +co{s}^{2}\theta =1\)
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