Question

If $\frac{cos\theta }{a}=\frac{sin\theta }{b}$, then $\frac{a}{sec2\theta }+\frac{b}{cosec2\theta }$ is equal to

• A. $a$
• B. $b$
• C. $\frac{a}{b}$
• D. $a+b$

Answer 1

Answer: (A)

$a$

Given

$\frac{\cos \theta }{a}=\frac{\sin \theta }{b}$

$\Rightarrow \frac{b}{a}=\tan \theta$

$a\cos 2\theta +b\sin 2\theta$

$=a\times \frac{1-{\tan }^n\theta }{1+{\tan }^n\theta }+b\times \frac{2\tan \theta }{1+\tan \theta }$

$=a$