Introduction to Trigonometry
CH08 Question Bank
CBSE_CH08_QUESTION_BANK
Grade 10
Question:
Simplify: $\sin^4\theta - \cos^4\theta$ in terms of $\sin^2\theta$ and $\cos^2\theta$ only, and then reduce it to a single trigonometric term.
Step-by-Step Solution
Key Concept: Factorise as a difference of squares, then apply the Pythagorean identity.
$\sin^4\theta-\cos^4\theta=(\sin^2\theta-\cos^2\theta)(\sin^2\theta+\cos^2\theta)$. [1.0 Mark]
Since $\sin^2\theta+\cos^2\theta=1$, this simplifies to $\sin^2\theta-\cos^2\theta$. [1.0 Mark]
This can also be written as $1-2\cos^2\theta$ (substituting $\sin^2\theta=1-\cos^2\theta$). [1.0 Mark]
Correct Answer:
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