Question

prove that cosec^2A-1/cosec^2A =cos^2A

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Answer 1

Step-by-step explanation:

cosec^2 A-1/cosec^2 A =cos^2 A

cot^2 A/cosec ^2 A = cos ^2 A. { cosec^2 A-1 = cot ^2 A}

cos^2 A { cot A = cos A/sin A}

sin^2 A. = cos^2 A

1. { cosec A = 1/sin A }

sin^2 A

since denominators are same they will be cancelled.

Then,

cos ^2 A. = cos ^2 A

1

cos ^2 A = cos^2 A

:.Hence proved

Answer 2

Answer:

Step-by-step explanation:

cosec^2 A-1/cosec^2 A =cos^2 A

cot^2 A/cosec ^2 A = cos ^2 A. { cosec^2 A-1 = cot ^2 A}

cos^2 A { cot A = cos A/sin A}

sin^2 A. = cos^2 A

1. { cosec A = 1/sin A }

sin^2 A

since denominators are same they will be cancelled.

Then,

cos ^2 A. = cos ^2 A

1

cos ^2 A = cos^2 A

:.Hence proved