Chapter 5: Q.8 (page 495)

Double-angle identities: Use double-angle identities to rewrite each of the following trigonometric expressions until no exponents are involved.
$\sin^{4} x =____$

Short Answer

Expert verified

$\sin^{4} x = \frac{1}{4} + \frac{\cos 4 x + 1}{8} - \frac{\cos 2 x}{2}$

Step by step solution

Step 1. Given information.

Consider the given information,

$\sin^{4} x =____$

Step 2. Explanation.

Write the given trigonometric expression in simplified form.

$\begin{array}{l} \sin^{4} x = {(\sin^{2} x)}^{2} \\ = {(\frac{1 - \cos 2 x}{2})}^{2} \\ = \frac{1 + \cos^{2} 2 x - 2 \cos 2 x}{4} \\ = \frac{1}{4} + \frac{\frac{\cos 4 x + 1}{2}}{4} - \frac{\cos 2 x}{2} \\ = \frac{1}{4} + \frac{\cos 4 x + 1}{8} - \frac{\cos 2 x}{2} \end{array}$

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Double-angle identities: Use double-angle identities to rewrite each of the following trigonometric expressions until no exponents are involved.
$\sin^{4} x =____$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explanation.

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Double-angle identities: Use double-angle identities to rewrite each of the following trigonometric expressions until no exponents are involved. sin4x=____

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explanation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Pure Maths

Probability and Statistics

Mechanics Maths

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Double-angle identities: Use double-angle identities to rewrite each of the following trigonometric expressions until no exponents are involved.
$\sin^{4} x =____$