Question

prove that:cosec^4A-1/cot^4A=1+2tan^2A​

Answer 1

cosec4A(1−cos4A)−2cot2A

=cosec4A(12−(cos2A)2)−2cot2A

=cosec4A((1+cos2A)(1−cos2A))−2cot2A

=cosec4A((1+cos2A)sin2A)−2cot2A

=1+cos2Asin2A−2cot2A

=cosec2A+cot2A−2cot2A

=cosec2A−cot2A

= 1 plus cot ^2 A is equal to cosec2A

therefore the answer is 1

Answer 2

Answer:

cosec4A(1−cos4A)−2cot2A

=cosec4A(12−(cos2A)2)−2cot2A

=cosec4A((1+cos2A)(1−cos2A))−2cot2A

=cosec4A((1+cos2A)sin2A)−2cot2A

=1+cos2Asin2A−2cot2A

=cosec2A+cot2A−2cot2A

=cosec2A−cot2A

Note:

1+cot2A=cosec2A

=1