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Trigonometry — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsTrigonometry2 Marks
Question
Prove that: $\sin^4\theta + \cos^4\theta = 1 - 2sin^2\theta \cos^2\theta .$
✓

Answer

$LHS = (\sin^2\theta )^2 + (\cos^2\theta )^2 + 2 \sin^2\theta \cos^2\theta - 2 \sin^2\theta \cos^2\theta$
$= ( \sin^2\theta + \cos^2\theta )^2- 2 \sin^2\theta \cos^2\theta$
$= 1 - 2 \sin^2\theta \cos^2\theta$
$= RHS$
Hence proved.

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