If a sin x+b cos (x+θ)+b cos (x-θ)=d for some real x, then the minimum value of | cos θ| is

Question

If a sin x+b cos (x+θ)+b cos (x-θ)=d for some real x, then the minimum value of | cos θ| is (A) (1/2|b|) √d2-a2 (B) (1/2|a|) √d2-a2 (C) (1/2|d|) √d2-a2 (D) (1/|a|) √d2-a2

Tardigrade Admin · Accepted Answer

Correct answer is (a) (1/2|b|) √d2-a2

Q. If $a sin x + b cos (x + θ) + b cos (x - θ) = d$ for some real $x$ , then the minimum value of $∣ cos θ ∣$ is

$\frac{1}{2∣ b ∣} d^{2} - a^{2}$

$\frac{1}{2∣ a ∣} d^{2} - a^{2}$

$\frac{1}{2∣ d ∣} d^{2} - a^{2}$

$\frac{1}{∣ a ∣} d^{2} - a^{2}$

Correct answer is (a) $\frac{1}{2∣ b ∣} d^{2} - a^{2}$

Q. If asinx+bcos(x+θ)+bcos(x−θ)=d for some real x, then the minimum value of ∣cosθ∣ is

2∣b∣1​d2−a2​

2∣a∣1​d2−a2​

2∣d∣1​d2−a2​

∣a∣1​d2−a2​