## anonymous 3 years ago Add and Simplify (cos(x)/Sin(x))+(Sin(x)/Cos(x))

1. anonymous

whats our common denominator? sin cos x right? can you try to continue? cos x sin x ----- + ------ = ------------ sin x cos x sin x cos x

2. anonymous

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3. anonymous

$\cos x \sin ^{2}x \times \frac{ 1 }{ \sin x \cos x }$

4. anonymous

cos x sin x cos x(cos x) +sin x(sin x) ----- + ------ = ---------------------------- sin x cos x sin x cos x

5. anonymous

oh oops forgot to multiply both fractions

6. anonymous

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7. anonymous

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8. anonymous

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9. anonymous

alternate solution multiply them with something that will make a common denominator we wanted to have a common denominator of sin x cos x therefore cos x cos x sin x sin x (cos x )^2 + (sin x)^2 1 ----- . ------- + ------ .----- = ------------------------ = ------------ sin x cos x cos x sin x sin x cos x sin x cos x whats 1/sin x =? also 1/cos x ?

10. anonymous

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11. anonymous

12. anonymous

yesss 1 1 1 csc x sec x = ----------- = -------- --------- or = ------- or = ------ or= csc x sec x sin x cos x sin x cos x cos x sin x

13. anonymous

Although i don't see how you get COS(X)^2 + SIN(X)^2 1 ----------------- = --------------- SIN(X) COS(X) SIN(X) COS(X)

14. anonymous

isnt it the identity (sin x)^2 + (cos x)^2 = 1 ??

15. anonymous

16. anonymous

Thanks again

17. anonymous

ok = 1/ sin x cos x = csc x/ cos x = sec x / sin x = sec x csc x

18. anonymous

yw... have fun now solving.. :D poist some more if you got stuck again :D