Question

Question #24406

Answer 1

`LHS=(sina-cosa+1)/(sina+cosa-1)`

As in the numerator of RHS is `cosa`, we multiply `cosa` with both numerator and denominator of LHS and proceed to simplify it to get the expression of RHS.

So `LHS=(cosa(sina-cosa+1))/(cosa(sina+cosa-1))`

`=(cosa(sina-cosa+1))/(cosa*sina+cos^2a-cosa))`

`=(cosa(sina-cosa+1))/(cosa*sina+1-sin^2a-cosa)`

`=(cosa(sina-cosa+1))/((1-sina)(1+sina)-cosa+cosasina)`

`=(cosa(sina-cosa+1))/((1-sina)(1+sina)-cosa(1-sina))`

`=(cosa(cancel(sina-cosa+1)))/((1-sina)(cancel(sina-cosa+1)))`

`=cosa/(1-sina)=RHS`