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Trigonometric Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Functions1 Mark
MCQ
Choose the correct answer. $\cos2\theta\cos2\phi+\sin^2(\theta-\phi)-\sin^2(\theta+\phi)$ is equal to:
  • A
    $\sin2(\theta+\phi)$
  • ✓
    $\cos2(\theta+\phi)$
  • C
    $\sin2(\theta-\phi)$
  • D
    $\cos2(\theta-\phi)$
✓

Answer

Correct option: B.
$\cos2(\theta+\phi)$
$\cos2\theta\cos2\phi+\sin^2(\theta-\phi)-\sin^2(\theta+\phi)$
$=\cos2\theta\cos2\phi+\sin(\theta-\phi+\theta+\phi)\sin(\theta-\phi-\theta-\phi)$
$=\cos2\theta\cos2\phi-\sin2\theta\sin2\phi$
$=\cos(2\theta+2\phi)$
$=\cos2(\theta+\phi)$

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