Question

Prove that cot^2 theta -tan^2 = cosec^2 theta - sec^2 theta

Answer 1

Hey !!!

Solution :-

from LHS

cot²¢ - tan²¢

we know that ,

cot²¢ = cosec²¢ - 1
tan²¢ = sec²¢ - 1

hence ,. cosec²¢ - 1 - (sec²¢ - 1 )

cosec²¢ - 1 - sec²¢ + 1

cosec²¢ - sec²¢ RHS prooved ..
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Hope it helps you !!

@Rajukumar111

Answer 2

Hi ,

Here I am using A instead of theta .

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we know the trigonometric identity

1 ) cot² A = cosec² A - 1

2 ) tan² A = sec² A - 1

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LHS = cot² A - tan² A

= ( cosec² A - 1 ) - ( sec² A - 1 )

= cosec² A - 1 - sec² A + 1

= cosec² A - sec² A

= RHS

Hence proved .

I hope this helps you.

: )