SOLUTION: Prove that 2sec^2x-2tan^2x/cscx = sin2x secx Link to equation composition: https://gyazo.com/f0b657e626aa9ca7f5c867958f237ad9

Algebra ->  Functions -> SOLUTION: Prove that 2sec^2x-2tan^2x/cscx = sin2x secx Link to equation composition: https://gyazo.com/f0b657e626aa9ca7f5c867958f237ad9      Log On


   

Question 1205302: Prove that 2sec^2x-2tan^2x/cscx = sin2x secx
Link to equation composition: https://gyazo.com/f0b657e626aa9ca7f5c867958f237ad9
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
%282sec%5E2%28x%29-2tan%5E2%28x%29%29%2Fcsc%28x%29+=+sin%282x%29+sec%28x%29

manipulate both sides
%282sec%5E2%28x%29-2tan%5E2%28x%29%29%2Fcsc%28x%29+=sin%282x%29+sec%28x%29
2%28sec%5E2%28x%29-tan%5E2%28x%29%29%2Fcsc%28x%29+=sin%282x%29+sec%28x%29

use identities: csc%28x%29=1%2Fsin%28x%29,sec%5E2%28x%29=1%2Fcos%5E2%28x%29, tan%5E2%28x%29=sin%5E2%28x%29%2Fcos%5E2%28x%29,sin%282x%29=2cos%28x%29%2Asin%28x%29, sec%28x%29=1%2F+cos%28x%29

...simplify

2sin%28x%29%28%281-sin%5E2%28x%29%29%2Fcos%5E2%28x%29%29=2sin%28x%29

2sin%28x%29%28%28cos%5E2%28x%29%29%2Fcos%5E2%28x%29%29=2sin%28x%29
2sin%28x%29=2sin%28x%29