Question

${\displaystyle \frac{{\cos }^2\theta }{{\sin }^2\theta }-\frac{1}{{\sin }^2\theta }}$, in simplified form, is ______.

विकल्प

• tan² θ

• sec² θ

• 1

• –1

Answer 1

${\displaystyle \frac{{\cos }^2\theta }{{\sin }^2\theta }-\frac{1}{{\sin }^2\theta }}$, in simplified form, is –1.

Explanation:

${\displaystyle \frac{{\cos }^2\theta }{{\sin }^2\theta }-\frac{1}{{\sin }^2\theta }}$

= ${\displaystyle \frac{{\cos }^2\theta -1}{{\sin }^2\theta }}$

= ${\displaystyle \frac{-{\sin }^2\theta }{{\sin }^2\theta }}$       ...(∵ sin²θ = 1 – cos²θ)

= –1