Question:
If \(\cos^{-1}x-\cos^{-1}\frac{y}{2}=\alpha\), then
\(4x^2-4xy\cos\alpha+y^2\) is equal to
If \(\cos^{-1}x-\cos^{-1}\frac{y}{2}=\alpha\), then
\(4x^2-4xy\cos\alpha+y^2\) is equal to
Show Hint
Use cosine rule identities for inverse trig equations.
Updated On: Mar 23, 2026
- \(2\sin2\alpha\)
- \(4\)
- \(4\sin^2\alpha\)
- \(4-4\sin^2\alpha\)
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The Correct Option is B
Solution and Explanation
Step 1: Let \(\cos^{-1}x=A,\ \cos^{-1}\frac{y}{2}=B\).
Step 2: Given \(A-B=\alpha\).
Step 3: Using cosine formula: \[ \cos(A-B)=x\cdot\frac{y}{2}+\sqrt{1-x^2}\sqrt{1-\frac{y^2}{4}} \]
Step 4: Simplification gives: \[ 4x^2-4xy\cos\alpha+y^2=4 \]
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