# What is sin(x)+cos(x) in terms of sine?

##### 2 Answers

Please see two possibilities below and another in a separate answer.

#### Explanation:

**Using Pythagorean Identity**

**Using complement / cofunction identity**

I've learned another way to do this. (Thanks Steve M.)

#### Explanation:

Suppose that

Then

# =(Rcosalpha)sinx+(Rsinalpha)cosx#

The coefficients of

Squaring and adding, we get

And now

so