Question

Verify the given identities. $$4 \sin x \cos ^{2} x=\sin 3 x+\sin x$$

   Verify the given identities.
$$4 \sin x \cos ^{2} x=\sin 3 x+\sin x$$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 6, Problem 74

Instant Answer

Solved by Expert Amit Srivastava

05/10/2020

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Step 1: We start with the right-hand side of the equation, which is $\sin 3x + \sin x$. Show more…

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Verify the given identities. $$4 \sin x \cos ^{2} x=\sin 3 x+\sin x$$

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Key Concepts

Double Angle Identity

Double angle identities express trigonometric functions of twice an angle in terms of the function of the original angle. For example, cosine squared can be rewritten using the identity cos²x = (1 + cos 2x)/2. This conversion is especially useful when eliminating higher-degree terms to facilitate simplification and verification of identities.

Trigonometric Identities

These are equations involving trigonometric functions that hold true for all values in the functions' domains. They serve as the foundational tools in trigonometry for simplifying expressions, solving equations, and establishing relationships between different trigonometric expressions.

Sum-to-Product Identities

Sum-to-product identities convert sums or differences of sine or cosine functions into products of trigonometric functions. These identities are particularly helpful in combining or simplifying expressions by reducing them to a form where factorization, cancellation, or further transformation becomes more straightforward.

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