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

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

BITSAT 2012

Exam: BITSAT
Year: 2012
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

BITSAT 2012 · Mathematics · Trigonometric Ratios & Identities

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

\sin ^{2} \theta+\sin ^{2} \phi=1 / 2, \cos ^{2} \theta+\cos ^{2} \phi=3 / 2,

then

\cos ^{2}(\theta-\phi)

is equal to

Options

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

Correct answer

B. $5 / 8$

Step-by-step 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}

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