If cosx + cos2x = 1, then the numerical value of (sin12x + 3 sin10x + 3 sin8x + sin6x - 1) is
0
1
-1
2
The value of 152 (sin 30° + 2 cos2 45° + 3 sin 30° + 4 cos2 45° +...+17 sin 30° + 18 cos2 45°) is
an integer but not a perfect square
a rational number but not an integer
a perfect square of an integer
irrational
(1 + sin α) (1 + sin β) (1 + sin γ) = (1 - sin α) (1 - sin β) (1 - sin γ), then each side is equal to
A.
Let (1 + sin α) (1 + sin β) (1 + sin γ) = (1 - sin α) (1 - sin β) (1 - sin γ) = x.
∴ x. x = (1 + sin α) (1 + sin β) (1 + sin γ) (1 - sin α) (1 - sin β) (1 - sin γ)
x2 = (1 - sin2α) (1 - sin2β) (1 - sin2γ)
x2 = cos2α . cos2β . cos2γ