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

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The given equation is equivalent to

This can be written as

The general solution of this equation ls

So,

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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]}

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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:

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Use trig identity:

We get:

Trig table and unit circle give -->

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