Question

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

• A. $\frac{1}{2|b|} \sqrt{d^2-a^2}$
• B. $\frac{1}{2|a|} \sqrt{d^2-a^2}$
• C. $\frac{1}{2|d|} \sqrt{d^2-a^2}$
• D. $\frac{1}{|a|} \sqrt{d^2-a^2}$

Answer 1

Answer: (A)

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