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# Prave that: sec 4 θ − cos 4 θ = 1 − 2 cos 2 θ - Geometry

ConceptApplication of Trigonometry

#### Question

Prove that:
$\sec^4 \theta - \cos^4 \theta = 1 - 2 \cos^2 \theta$

#### Solution

Disclaimer: There is printing mistake in the question. The correct question should be

$\sin^4 \theta - \cos^4 \theta = 1 - 2 \cos^2 \theta$.
The solution has been provided accordingly.
$\sin^4 \theta - \cos^4 \theta$
$= \left( \sin^2 \theta \right)^2 - \left( \cos^2 \theta \right)^2$
$= \left( \sin^2 \theta - \cos^2 \theta \right)\left( \sin^2 \theta + \cos^2 \theta \right) \left[ a^2 - b^2 = \left( a + b \right)\left( a - b \right) \right]$
$= \sin^2 \theta - \cos^2 \theta \left( \sin^2 \theta + \cos^2 \theta = 1 \right)$
$= 1 - \cos^2 \theta - \cos^2 \theta$
$= 1 - 2 \cos^2 \theta$
Is there an error in this question or solution?

#### APPEARS IN

Solution Prave that: sec 4 θ − cos 4 θ = 1 − 2 cos 2 θ Concept: Application of Trigonometry.
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