36 csc40 39 3 sin 0 4 cos 0 3 cos2 0 Solution36 csc4 csc2

36. csc40 39. 3 sin 0 4 cos 0 3 cos2 0

Solution

36) csc⁴ - csc² = cos⁴ + cot²

consider csc⁴ - csc² = csc²[csc² -1]

==> csc²[cot² ]        since csc² - cot² = 1 ==> csc² = 1 + cot² , csc² -1 = cot²

==> (1 + cot²)(cot²)

==> cot⁴ + cot²

Hence csc⁴ - csc² = cos⁴ + cot²

39) 3sin² + 4cos² = 3 + cos²

consider 3sin² + 4cos²

==> 3sin² + 3cos² + cos²

==> 3(sin² + cos²) + cos²

==> 3(1) + cos²

==> 3 + cos²

Hence 3sin² + 4cos² = 3 + cos²