Question

If $\theta$ and $\varphi$ are complementary angles then find the value of $\frac{cosec\theta }{\sin \theta }-{\tan }^2\varphi$.

Answer 1

Given $\theta$ and $\varphi$ are complementary then $\theta +\varphi ={90}^o$......(1).

Now,

$\frac{cosec\theta }{\sin \theta }-{\tan }^2\varphi$

$=cose{c}^2\theta -{\tan }^2({90}^o-\varphi )$

$=cose{c}^2\theta -{\cot }^2\varphi$

$=1$.