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Trigonometry Practice Test 1

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Question : 21 of 40

Marks: +1, -0

What is the value of

\frac{\sin^3 x + \cos^3 x}{\sin x + \cos x} + \sin x \cos x?

0
sin x
cos x
1
None of these

Solution: 👈: Video Solution

Concept:

Use the factorization of a sum of cubes and the identity

\sin^2 x+\cos^2 x=1

.

Explanation:

Let the given expression be

E

.

Factor

\sin^3 x+\cos^3 x

as

(\sin x+\cos x)(\sin^2 x-\sin x\cos x+\cos^2 x)

.

Since

\sin^2 x+\cos^2 x=1

, this equals

(\sin x+\cos x)(1-\sin x\cos x)

.

Cancel

\sin x+\cos x

in the fraction, assuming

\sin x+\cos x\ne0

.

Then

E=1-\sin x\cos x+\sin x\cos x

.

So

E=1

.

Answer:

1

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