Question

cosec^4 A(1-cos^4 A) – 2 cot^2A=​

Answer 1

cosec4A(1−cos4A)−2cot2Acos⁡ec4A(1−cos4A)−2cot2A

=cosec4A(12−(cos2A)2)−2cot2A=cos⁡ec4A(12−(cos2A)2)−2cot2A

=cosec4A((1+cos2A)(1−cos2A))−2cot2A=cos⁡ec4A((1+cos2A)(1−cos2A))−2cot2A

=cosec4A((1+cos2A)sin2A)−2cot2A=cos⁡ec4A((1+cos2A)sin2A)−2cot2A

=1+cos2Asin2A−2cot2A=1+cos2Asin2A−2cot2A

=cosec2A+cot2A−2cot2A=cos⁡ec2A+cot2A−2cot2A

=cosec2A−cot2A=cos⁡ec2A−cot2A

Note:

1+cot2A=cosec2A1+cot2A=cos⁡ec2A

=1=1

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