# How do you solve #\sin 2x + \cos ( - x ) = 0#?

##### 2 Answers

In the interval

#### Explanation:

It helps to know what range that

Cosine is an even function, so rewrite as

Isolate cosine to the left-hand side. Subtract

Express the right hand side in terms of cosine. Rewrite the right-hand side using

Taking the inverse cosine of both sides reveals that the arguments are equal to each other.

Solve for

In the interval

Use double angle identity for sine and even-odd function for cosine, then factor and solve.

Answer:

#### Explanation:

Solve

Consider the following identities:

Double angle identity for sine:

#sin2x=2sinxcosx# Even-odd identity for cosine:

#cos(-x)=cos(x)#

We can substitute these identities into the original equation:

We can factor out a

So we have that