SOLUTION: sec x + cos x = 3,then tan^2 x - sin^2 x is

Algebra ->  Trigonometry-basics -> SOLUTION: sec x + cos x = 3,then tan^2 x - sin^2 x is      Log On


   

Question 715282: sec x + cos x = 3,then tan^2 x - sin^2 x is
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
sec+x+%2B+cos+x+=+3%2Cthen+tan%5E2+x+-+sin%5E2+x+is

secx +cosx =3
square both sides
sec%28x%29%2Bcos%28x%29%29%5E2=+9
sec%5E2%28x%29+%2B2sec%28x%29cos%28x%29%2Bcos%5E2%28x%29=9
sec^2x= 1+tan^2x: cos^2x = 1-sin^2x
1%2Btan%5E2%28x%29+%2B2+%2B1-sin%5E2%28x%29=9

tan%5E2%28x%29-sin%5E2%28x%29=+9-4
tan%5E2%28x%29-sin%5E2%28x%29+=+5