How to prove that : 1-cos^4A/sin^4A= 1 + 2cot^2A?
1 Answer
Mar 30, 2018
This identity is FALSE
Explanation:
Putting on a common denominator, we get:
(sin^4A - cos^4A)/sin^4A = 1 + 2cot^2A
((sin^2A + cos^2A)(sin^2A - cos^2A))/sin^4A = 1 + 2cot^2A
(sin^2A - cos^2A)/sin^4A = 1+ 2cos^2A/sin^2A
(sin^2A - (1 - sin^2A))/sin^4A = 1 + 2(cos^2A/sin^2A)
(2sin^2A - 1)/sin^4A =(sin^2A + 2cos^2a)/sin^2A #(2sin^2A - 1)/sin^4A = (sin^2A + 2(1- sin^2A))/sin^2A
(2sin^2A - 1)/sin^4A = (2 - sin^2A)/sin^2A
2/sin^2A - 1/sin^4A = 2/sin^2A - 1
And since
Hopefully this helps!