Multiple Choice QuestionsIf a sin θ + b cos θ = c, then the value of a cos θ - b sin sin θ is
D.
a sin θ + b cos θ = c
On squaring both sides, we get,
a2 sin2 θ + b2 cos2θ + 2 ab sin θ cos θ = c2
⟹ a2(1 - cos2θ) + b2(1 - sin2θ) + 2ab sinθ cos θ = c2
⟹ a2 - a2cos2θ + b2 - b2 sin2θ + 2 ab sin θ cos θ = c2
On rearragning, we get
a2 + b2 - c2 = a2 cos2θ + b2 sin2θ - 2 ab sinθ cosθ
⟹ a2 +b2 - c2 = (a cosθ - b sinθ)2
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
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and 
where A > B > 0 and A + B is an acute angle, then the value of B is
