Maharashtra State Board course SSC (English Medium) Class 10th Board Exam
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Prave that: sec 4 θ − cos 4 θ = 1 − 2 cos 2 θ - Geometry

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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?

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