Q. If 7 $\cos{x - 24\sin{x = \ \lambda\cos{(x + \alpha),\ 0 < \alpha < \frac{\pi}{2}}}},$ be true for all $x\ \in R,$ then
A) $\lambda = 25$
B) $\alpha = \sin^{- 1}\frac{21}{25}$
C) $\lambda = - 25$
D) $\alpha = \cos^{- 1}\frac{17}{25}$
Explanation
(a)
$Given,\ 7\cos{x - 24\sin{x = \lambda\cos{(x + \alpha)}}}$
$\Rightarrow 25\left( \frac{7}{25}\cos{x - \frac{24}{25}}\sin x \right) = \lambda\cos{(x + \alpha)}$
$\Rightarrow \ 25\lbrack\cos{(\beta + x) = \lambda\cos(x + \alpha)}$
Where $\cos{\beta = \frac{7}{25}}$
$\Rightarrow \ \lambda = 25$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.