Question

If $\sin^2 \theta + \sin^2 \phi = 1/2, \cos^2 + \cos^2 \phi = 3/2$, then $\cos^2 (\theta - \phi)$ is equal to

• A. 44628
• B. 44689
• C. 44624
• D. 44685

Answer 1

Answer: (B)

44689

Answer 2

Using cosine formula
$2 \sin (\theta + \phi) \cos (\theta - \phi) = 1/2$ ......(i)
$2 \cos (\theta + \phi) \cos (\theta - \phi) = 3/2$ .....(ii)
Squaring (1) and (2) and then adding
$4 \cos^{2} \left(\theta - \phi\right) = \frac{1}{4} + \frac{9}{4} = \frac{5}{2}$
$\Rightarrow \cos^{2} \left(\theta -\phi\right) = \frac{5}{8}$