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Chapter 5: Problem 33

Perform the multiplication and use the fundamental identities to simplify. There is more than one correct form of each answer. $$(\sin x+\cos x)^{2}$$

Short Answer

Expert verified
The simplified form of the expression is \(1 + 2\sin x \cos x\).

Step by step solution

01

Recognize the Binomial Square

This is a form of a binomial square, \((a+b)^2 = a^2 + 2ab + b^2\). By substituting \(a = \sin x\) and \(b = \cos x\), the expression becomes {\(\sin^2 x + 2\sin x \cos x + \cos^2 x\)}.
02

Use Trigonometric Identities

We have a trigonometric identity \(\sin^2 x + \cos^2 x = 1\). By substituting this identity into our expression, it simplifies to \(1 + 2\sin x \cos x\).
03

Formula Representation

The final, simplified expression is {\(1 + 2\sin x \cos x\)}.

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Most popular questions from this chapter

Proof (a) Write a proof of the formula for \(\sin (u+v)\) (b) Write a proof of the formula for \(\sin (u-v)\)

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