SOLUTION: (Sinx+tanx)(sinx÷1+cosx)=sinx×tanx prove the identity

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Question 974152: (Sinx+tanx)(sinx÷1+cosx)=sinx×tanx prove the identity
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
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%28Sinx%2Btanx%29%28sinx%2F%281%2Bcosx%29%29=sinx%2Atanx

%28sin%28x%29%2Bsin%28x%29%2Fcos%28x%29%29%28sin%28x%29%2F%281%2Bcos%28x%29%29%29





%28sin%28x%29cos%28x%29%2Bsin%28x%29%29%2F%281%2Bcos%28x%29%29%2Atan%28x%29

Try multiplic by %281-cos%28x%29%29%2F%281-cos%28x%29%29.





%28%28sin%28x%29cos%28x%29%2Bsin%28x%29%29%281-cos%28x%29%29%2Fsin%5E2%28x%29%29tan%28x%29



%28%28sin%28x%29-sin%28x%29cos%5E2%28x%29%29%2Fsin%5E2%28x%29%29%2Atan%28x%29

%28sin%28x%29%281-cos%5E2%28x%29%29%2Fsin%5E2%28x%29%29%2Atan%28x%29

%28sin%28x%29%2Asin%5E2%28x%29%2Fsin%5E2%28x%29%29tan%28x%29

%28sin%28x%29%2Across%28sin%5E2%28x%29%29%2Fcross%28sin%5E2%28x%29%29%29tan%28x%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

(Sinx+tanx)(sinx÷1+cosx)=sinx×tanx prove the identity 


The left-side will be made equivalent to the right-side

 --------- Converting tan x to sin+x%2Fcos+x

 ---- Multiplying by LCD, cos x

 ---------- Factoring out GCF, sin x, in numerator

 ------- Cancelling 1 + cos x in numerator and denominator

%28%28sin+x%29%2F%28cos+x%29%29+%2A+sin+x+=+%28sin+x%29%28tan+x%29, or %28sin+x%29+%2A+%28%28sin+x%29%2F%28cos+x%29%29+=+%28sin+x%29%28tan+x%29 

%28sin+x%29+%2A+highlight%28tan+x%29+=+%28sin+x%29%28tan+x%29 -------- Converting %28sin+x%29%2F%28cos+x%29 to tan x

As seen, the left and right sides are congruent, hence the identity has been proven.