# How do you solve #sinx+cosx=1#?

##### 3 Answers

#### Answer:

#### Explanation:

The given equation is equivalent to

This can be written as

The general solution of this equation ls

So,

Having noted that there were 40K viewers for the answers by me,

Hero and Nghi, I think I could invoke more interest by including the

solutions for

cos x, when

For cos x - sin x = 1,

the general solution is

Note the change in the multiple from

For

See x-intercepts as graphical solutions.

Graph on uniform scale for solutions

graph{y-cos x - sin x +1 = 0[-7 7 -3 4]}

Graph on uniform scale for solutions

graph{y-cos x + sin x +1 = 0[-7 7 -3 4]}

See combined graph for solutions

graph{(y- sec x - tan x +1)(y- sec x+ tan x +1)=0[-13 13 -6.5 6.5]}

#### Answer:

#### Explanation:

If

Using the identities:

The equation can be simplified to:

Therefore

The values of

But here

However, since we squared the equation, we need to check all of these answers work in the original equation:

When we get to

This can be written as:

#### Answer:

#### Explanation:

Use trig identity:

We get:

Trig table and unit circle give -->