Question

"Question44
Prove the identity : (1 - cos² θ ) cosec² θ = 1
Chapter7,Trigonometric identities Exercise -7A , Page number 314"

Answer 1

Hey !!!

So simple question .

from LHS

( 1 - cos²¢ ) cosec²¢

or, sin²¢ * cosec²¢ ➡ { 1 - cos²¢ = sin²¢ }

or,
sin²¢/sin²¢ ➡ {•°•1/cosec²¢ = sin²¢ }

= 1 RHS prooved

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Hope it helps you !

@Rajukumar111

Answer 2

Hey there!

We know that,

( sin²θ + cos² θ ) = 1

sin²θ = 1 - cos²θ

Also , sinθ = 1 / cosecθ

Coming back to your question :

L. H. S

=> (1 - cos² θ ) cosec² θ

=> sin² θ ( cosec² θ )

=> ( sin θ . cosec θ )²

=> ( cosec θ / cosec θ ) ²

=> 1²

=> 1

=> R. H. S


$\therefore$ We proved that (1 - cos² θ ) cosec² θ = 1