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Question
MathsClass 10

\( \frac{cos\left(90°-\theta \right)cos\theta }{tan\theta }+\frac{co{s}^{2}(90°-\theta )}{1}=\)
(A) 0
(B) 1
(C) 2
(D) 3

Answer

(B)
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Solution

\( \therefore\;cos\left(90°-\theta \right)=sin\theta   \)
\( \frac{cos\left(90°-\theta \right)cos\theta }{tan\theta }+co{s}^{2}(90°-\theta )\)
\( =\frac{sin\theta\;cos\theta }{tan\theta }+\frac{si{n}^{2}\theta }{1}=\frac{sin\theta\;cos\theta +si{n}^{2}\theta\;tan\theta }{tan\theta }\)
\( =\frac{sin\theta (cos\theta +sin\theta\;tan\theta )}{tan\theta }=\frac{sin\theta (cos\theta +sin\theta  \frac{sin\theta }{cos\theta }}{tan\theta }\)
\( =\frac{sin\theta \left(\frac{co{s}^{2}\theta +si{n}^{2}\theta }{cos\theta }\right)}{tan\theta }=\frac{\frac{sin\theta }{cos \theta }}{\frac{sin\theta }{cos\theta }}=1\)
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