If sin^2 θ+sin^2 φ=1 / 2, cos^2 θ+cos^2 φ=3 / 2, then cos^2(θ-φ) is equal to

Correct answer: (B) 5 / 8. Using cosine formula 2 sin (θ+φ) cos (θ-φ)=1 / 2 ...(i) 2 cos (θ+φ) cos (θ-φ)=3 / 2 ...(ii) Squaring (1) and (2) and then adding cos^2(θ-φ)=1/4+9/4=5/2 ⇒ cos^2(θ-φ)=5/8

Q43 / 125 · BITSAT 2012 · Mathematics

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

A
$3 / 8$
Correct answer
B
$5 / 8$
C
$3 / 4$
D
$5 / 4$

Solution

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 $\cos ^{2}(\theta-\phi)=\frac{1}{4}+\frac{9}{4}=\frac{5}{2} \Rightarrow \cos ^{2}(\theta-\phi)=\frac{5}{8}$

Hence, the correct answer is option: 'B'.

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

Solution

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