Question

if cos theta + cos square theta is equal to 1 prove that sin to the power 12 70 + 3 into sin to the power 10 theta + 3 into 10 to the power 8 70 + 2 into sin to the power 4 theta + 2 sin square minus 2 is equal to 1 ​

Answer 1

Consider, sin6ө + cos6ө =1-3sin2өcos2ө (sin2ө)3 +(cos2ө)3 = (sin2ө + cos2ө)3 − 3 (sin2ө cos2ө)(sin2ө + cos2ө)   [since a + b = (a+b)3 − 3ab(a+b)]                           = 1 − 3sin2өcos2ө    [Since sin2ө +cos2ө = 1]