SOLUTION: Prove that sinxtanx + sinx/tanx= 1/cosx

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Question 974277: Prove that sinxtanx + sinx/tanx= 1/cosx
Found 3 solutions by amarjeeth123, josgarithmetic, MathTherapy:
Answer by amarjeeth123(569) About Me  (Show Source):
You can put this solution on YOUR website!
LHS=sinxtanx + sinx/tanx
=sinx(tanx+1/tanx)
=sinx[(tanx)^2+1]/tanx
=sinx[(secx)^2](cosx)/sinx
=secx
=1/cosx=RHS

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
sinxtanx + sinx/tanx= 1/cosx

sin%28x%29tan%28x%29+%2B+sin%28x%29%2Ftan%28x%29=+1%2Fcos%28x%29

sin%28x%29sin%28x%29%2Fcos%28x%29%2Bsin%28x%29cos%28x%29%2Fsin%28x%29

sin%5E2%28x%29%2Fcos%28x%29%2Bsin%28x%29cos%28x%29%2Fsin%28x%29



%28sin%5E3%28x%29%2Bsin%28x%29cos%5E2%28x%29%29%2F%28cos%28x%29sin%28x%29%29

%28sin%5E2%28x%29%2Bcos%5E2%28x%29%29%2Fcos%28x%29 after canceling sin/sin...

Basic identity,
1%2Fcos%28x%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Prove that sinxtanx + sinx/tanx= 1/cosx
Left side will be made congruent to right side

%28sin+x%29%28tan+x%29+%2B+%28sin+x%29%2F%28tan+x%29+=+1%2Fcos+x+

%28sin+x%29+%2A+%28%28sin+x%29%2F%28cos+x%29%29+%2B+%28sin+x%29%22%F7%22%28sin+x%29%2F%28cos+x%29+=+1%2Fcos+x

%28sin+x%29+%2A+%28%28sin+x%29%2F%28cos+x%29%29+%2B+%28sin+x%29%22%2A%22%28cos+x%29%2F%28sin+x%29+=+1%2Fcos+x

%28sin+x%29+%2A+%28%28sin+x%29%2F%28cos+x%29%29+%2B+cross%28%28sin+x%29%29%22%2A%22%28cos+x%29%2Fcross%28%28sin+x%29%29+=+1%2Fcos+x

%28sin+x%29+%2A+%28%28sin+x%29%2F%28cos+x%29%29+%2B+cos+x+=+1%2Fcos+x

%28sin%5E2+%28x%29%29%2F%28cos+x%29+%2B+cos+x+=+1%2F%28cos+x%29

%28sin%5E2+%28x%29+%2B+cos%5E2+%28x%29%29%2Fcos+x+=+1%2Fcos+x

highlight_green%28highlight_green%281%2Fcos+x+=+1%2Fcos+x%29%29 ------- sin%5E2+%28x%29+%2B+cos%5E2+%28x%29+=+1