Question

Prove
Sec^2 + cosec^2
Sec^2 x cosec^2​

Answer 1

sec² + cosec² = 1/cos² + 1/sin².

= cos²+sin²/ cos²sin²

= 1/cos²sin²

= sec² cosec²

Answer 2

Step-by-step explanation:

Given : A trigonometric equation.

To Prove : $sec^2x+cosec^2x=sec^2x*cosec^2x$

Trigonometric identities used :

1. $sec^2x=\frac{1}{cos^2x}$
2. $cosec^2x=\frac{1}{sin^2x}$
3. $sin^2x+cos^2x=1$

• Proof :

We have,

⇒  $sec^2x+cosec^2x=sec^2x*cosec^2x$

taking L.H.S separately to solve equation,

⇒  $sec^2x+cosec^2x$

by using identity (1) and (2) we get,

⇒  $\frac{1}{cos^2x} +\frac{1}{sin^2x}$

taking L.C.M as $cos^2x*sin^2x$,

⇒  $\frac{sin^2x+cos^2x}{cos^2x*sin^2x}$

by using identity (3),

⇒  $\frac{1}{cos^2x*sin^2x}$

or   $\frac{1}{cos^2x} *\frac{1}{sin^2x}$

again using identity (1) and (2),

⇒  $sec^2x*cosec^2x$.

Hence proved, $L.H.S=R.H.S$ or  $sec^2x+cosec^2x=sec^2x*cosec^2x$ .