Question #3d30a

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Answer 1 · 2017-06-24T18:59:49

Multiply both sides by #sin(x)cos(x)#.

Here is how you can prove the identity is true. First, express all terms as either #sin(x)# or #cos(x)#

#(1/sin(x)+1/cos(x))/(sin(x)+cos(x))=cos(x)/sin(x)+sin(x)/cos(x)#

Then multiply both sides by #sin(x)cos(x)#

#sin(x)cos(x)xx(1/sin(x)+1/cos(x))/(sin(x)+cos(x))#
#=sin(x)cos(x)xx(cos(x)/sin(x)+sin(x)/cos(x))#

The left hand side multiplies #sin(x)cos(x)# through the numerator, giving

#(cos(x)+sin(x))/(sin(x)+cos(x))=1#

The right hand side multiplies #sin(x)cos(x)# though each term, giving

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

Because the left hand side equals the right hand side, the identity is proven.