## HelpMe94 3 years ago Add and Simplify (cos(x)/Sin(x))+(Sin(x)/Cos(x))

1. mark_o.

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. HelpMe94

|dw:1352421024901:dw|

3. HelpMe94

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

4. mark_o.

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

5. HelpMe94

oh oops forgot to multiply both fractions

6. HelpMe94

|dw:1352421346060:dw|

7. HelpMe94

|dw:1352421430067:dw|

8. HelpMe94

|dw:1352421617501:dw|

9. mark_o.

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. HelpMe94

|dw:1352421796900:dw|

11. HelpMe94

So the answer is CSC(X)SEC(X)

12. mark_o.

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. HelpMe94

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

14. mark_o.

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

15. HelpMe94

oh yeah your right

16. HelpMe94

Thanks again

17. mark_o.

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

18. mark_o.

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