SOLUTION: Prove that the following statement is an identity. 1) (sin x + tan x)/ (1+sec x) = sin x

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Question 439288: Prove that the following statement is an identity.
1) (sin x + tan x)/ (1+sec x) = sin x
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
%28sin%28x%29+%2B+tan%28x%29%29%2F+%281%2Bsec%28x%29%29 = sin x

use tan%28theta%29=sin%28theta%29%2Fcos%28theta%29 to replace tan%28x%29
and use sec%28theta%29=1%2Fcos%28theta%29 to replace sec%28x%29

%28sin%28x%29+%2B+sin%28x%29%2Fcos%28x%29%29%2F+%281%2B1%2Fcos%28x%29%29

Multiply both terms on top and the
term on the bottom by cos%28x%29

%28sin%28x%29cos%28x%29+%2B+sin%28x%29%29%2F%28cos%28x%29%2B1%29

Factor sin%28x%29 out on top

%28sin%28x%29%28cos%28x%29+%2B+1%29%29%2F%28cos%28x%29%2B1%29

Cancel the cos%28x%29%2B1's:

%28sin%28x%29%28cross%28cos%28x%29+%2B+1%29%29%29%2F%28cross%28cos%28x%29%2B1%29%29

and you're left with:

sin%28x%29

Edwin