L lotmasta New member Joined Jun 1, 2005 Messages 4 Jun 1, 2005 #1 Hi I'm having some trouble simplifying this: 1-cos x + tan^2 x - sec^2 x --------- sin^2 x I know that tan^2 - sec^2 x = -1 but I don't know what to do after getting 1-cos x --------- - 1 sin^2 x
Hi I'm having some trouble simplifying this: 1-cos x + tan^2 x - sec^2 x --------- sin^2 x I know that tan^2 - sec^2 x = -1 but I don't know what to do after getting 1-cos x --------- - 1 sin^2 x
S soroban Elite Member Joined Jan 28, 2005 Messages 5,584 Jun 1, 2005 #2 Hello, lotmasta! I don't know what to do after getting 1-cos x --------- - 1 sin^2 x Click to expand... We can simplify it a bit more . . . but it's not very satisfying. . . . 1 - cos x . . . . . . . . . . . .1 - cos x . . . . . . . . . . . . . . 1 . . . ------------ - 1 . = . -------------------------- - 1 . = . ------------ - 1 . . . 1 - cos<sup>2</sup>x . . . . . . . (1 - cos x)(1 + cos x) . . . . . . 1 + cos x Get a common denominator and combine: . . . . . . .1 . . . . 1 + cos x . . . . .1 - 1 - cos x . . . . . - cos x . . . ------------ - ------------ . = . ---------------- . = . ------------ . . . 1 + cos x . .1 + cos x . . . . . .1 + cos x . . . . . 1 + cos x . . . and that's all we can do.
Hello, lotmasta! I don't know what to do after getting 1-cos x --------- - 1 sin^2 x Click to expand... We can simplify it a bit more . . . but it's not very satisfying. . . . 1 - cos x . . . . . . . . . . . .1 - cos x . . . . . . . . . . . . . . 1 . . . ------------ - 1 . = . -------------------------- - 1 . = . ------------ - 1 . . . 1 - cos<sup>2</sup>x . . . . . . . (1 - cos x)(1 + cos x) . . . . . . 1 + cos x Get a common denominator and combine: . . . . . . .1 . . . . 1 + cos x . . . . .1 - 1 - cos x . . . . . - cos x . . . ------------ - ------------ . = . ---------------- . = . ------------ . . . 1 + cos x . .1 + cos x . . . . . .1 + cos x . . . . . 1 + cos x . . . and that's all we can do.
