Math

QuestionRewrite sinxcotx+cosx\sin x \cdot \cot x + \cos x using sinx\sin x and cosx\cos x, then simplify.

Studdy Solution

STEP 1

Assumptions1. We are given the expression sinxcotx+cosx\sin x \cdot \cot x+\cos x. . We are asked to write this expression in terms of sinx\sin x and cosx\cos x.
3. We know that cotx=cosxsinx\cot x = \frac{\cos x}{\sin x}.

STEP 2

First, we will replace cotx\cot x with cosxsinx\frac{\cos x}{\sin x} in the given expression.
sinxcotx+cosx=sinxcosxsinx+cosx\sin x \cdot \cot x+\cos x = \sin x \cdot \frac{\cos x}{\sin x}+\cos x

STEP 3

Now, we simplify the expression by cancelling out the common terms.
sinxcosxsinx+cosx=cosx+cosx\sin x \cdot \frac{\cos x}{\sin x}+\cos x = \cos x + \cos x

STEP 4

Finally, we combine like terms to simplify the expression.
cosx+cosx=2cosx\cos x + \cos x =2\cos xSo, the expression sinxcotx+cosx\sin x \cdot \cot x+\cos x simplifies to 2cosx2\cos x in terms of sinx\sin x and cosx\cos x.

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