How to solve for x?

Question

#sin (x+45) + sin (x-45) = 1#

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Answer 1 · 2017-07-25T16:19:57

#x=45^@+360k, k in ZZ#

#x=135^@+360k, k in ZZ#

#sin(x+45)+sin(x-45)=1#

Use the sum-to-product formulae:

#sinA+sinB=2sin((A+B)/2)cos((A+B)/2)#

#sin(x+45)+sin(x-45)=2sin((x+45+x-45)/2)cos((x+45-(x-45))/2)=2sinxcos45=sqrt2(sinx)=1#

#sinx=1/sqrt2#

#x=45^@+360k, k in ZZ#

#x=135^@+360k, k in ZZ#