Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesAddition, Multiplication, Subtraction formula based,Multiple/Submultiple anglesHard2 minPYQ_2012

MathematicsHardsingle choice

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

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Solution:

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

Stream:BITSATSubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Addition, Multiplication, Subtraction formula based,Multiple/Submultiple angles

⏱ 2mℹ️ Source: PYQ_2012

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