Question

NEED HELP.. FAST!!
Rewrite with only sin x and cos x.

cos 2x + sin x

Answer 1

Hello!

The answer is:

The rewritten expression is:

$cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)$

Why?

To solve this problem we need to use the trigonometric identity of the double angle for the cosine which states that:

$cos(2\alpha)=cos^{2}(\alpha)-sin^{2}(\alpha)$

Also, if we want to rewrite only with terms of cos(x) and sin(x), we can apply the following property:

$(a^{2} -b^{2})=(a+b)(a-b)$

So, rewriting the trigonometric equation, we have:

$cos^{2}(\alpha)-sin^{2}(\alpha)=(cos(x)+sin(x))*(cos(x)-sin(x))$

Then, we are given the expression:

$cos(2x)+sin(x)$

Now, rewriting the given expression with only sin(x) and cos(x), we have:

$cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)$

Hence, the answer is:

$cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)$

Have a nice day!