# How do you solve sin(x)+cos(x)=-1?

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We have an identity

Use this to find the value of

We got two values for

Put them one by one in equation-1.

Squaring both sides

Divide by two both sides

It gives

We get

The solution for this is

Here ,

Now , we also get

It gives

The solution for this is

If you put

Hope it helps :)

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Given:

Square both sides

Either

If

and

If

and

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- Square both sides

#(sin(x)+cos(x))^2=(-1)^2#

#sin(x)^2+cos^2x+2sinxcosx=1#

#1+2sinxcosx=1#

#2sinxcosx=0#

#2sinx(cosx)=0#

#sinx=0#

#cosx=0#

#x= pi+2pin, n∈Z#

#x= (3pi)/2+2pin, n∈Z#

#x=pi/2+2pin, n∈Z# EXTRANEOUS

#x=0+2pin, n∈Z# EXTRANEOUS

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