# Thread: Trigonometric Identity

1. ## Trigonometric Identity

Question was 'Proof this following identity' - I couldn't for the life of me simplify the LHS down to the RHS. If any one could provide a rudimentary break down of the LHS I would be very grateful.

((tanX)^2+(cosX)^2)/((sinX)+(secX)) = secX - sinX

2. ## Re: Trigonometric Identity

..ah dont worry, I was being silly - the numerator can be simplified to the difference of two squares.

3. ## Re: Trigonometric Identity

$\dfrac{\tan^2{x}+ 1-\sin^2{x}}{\sin{x}+\sec{x}}$

$\dfrac{\sec^2{x}-\sin^2{x}}{\sin{x}+\sec{x}}$

$\dfrac{(\sec{x}-\sin{x})(\sec{x}+\sin{x})}{\sin{x}+\sec{x}}$