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The numerical value of \( \Large \frac{5}{sec^{2} \theta }+\frac{2}{1+cot^{2} \theta }+3 \ sin^{2} \theta \) is


A) 5

B) 2

C) 3

D) 4

Correct Answer:
A) 5

Description for Correct answer:
\( \Large \frac{5}{sec^{2} \theta }+\frac{2}{1+cot^{2} \theta }+3 \ sin^{2} \theta \)

= \( \Large 5 \ cos^{2} \theta +\frac{2}{cosec^{2} \theta }+3 \ sin^{2} \theta \)

= \( \Large 5 \ cos^{2} \theta +2 \ sin^{2} \theta +3 \ sin^{2} \theta \)

= \( \Large 5 \ cos^{2} \theta +5 \ sin^{2} \theta \)

= \( \Large 5(sin^{2} \theta +cos^{2} \theta ) \)

= \( \Large 5 \times 1=5 \)

Part of solved Trigonometry questions and answers : >> Elementary Mathematics >> Trigonometry




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