## Christians4 2 years ago Prove: (sinx + cosx) (Tan^2x+1/tanx) = 1/cosx + 1/sinx Picture below for what it looks like properly

1. Christians4

tell me if you need clarification i can drop LS and RS

2. Christians4

3. lgbasallote

hmm seems i really can't figure out what you mean. maybe it's time to show the picture

4. Christians4

|dw:1352211230059:dw|

5. Christians4

|dw:1352211285143:dw|

6. lgbasallote

ahh

7. lgbasallote

here's a hint that might help: $\huge \tan^2 x + 1 = \sec^2 x$ and $\huge \sec^2 x = \frac1{\cos^2 x}$ try solving it

8. Christians4

sec

9. Christians4

I ended up getting (sinx+cosx) (1/cosxsinx) for my left side

10. Christians4

woo it worked

11. Christians4

How do I prove identities that are like this:

12. Christians4

1+tanx/1-tanx = Tan (x+pi/4)

13. myininaya

$\frac{1+\tan(x)}{1-\tan(x)}=\tan(x+\frac{\pi}{4})$ I would write each side so that the function tan( ) only contains x and not both x & x+pi/4. You the sum identity for tan. If you don't know it write both sides in terms of sine and cosine. Use the sum identities for them to expand tan(x+pi/4)

14. Christians4

sum identity for tan?

15. Christians4

I know the cos and sin ones

16. Christians4

is it just those over eachother?

17. Christians4

oops im confused.

18. Christians4

do u simply mean sinx/cosx?

19. phi

try using tan = sin/cos and see how it works out

20. Christians4

alright but on the R.S what do i do with the (x +pi/4)

21. myininaya

$\tan(x+\frac{\pi}{4})=\frac{\sin(x+\frac{\pi}{4})}{\cos(x+\frac{\pi}{4})}$ Use sum identity for sine and cosine.

22. phi

remember sin(a+b)= sin(a)cos(b) + cos(a) sin(b) and cos(a+b)= cos(a)cos(b)- sin(a)sin(b)

23. Christians4

I plugged in the sum identity but i dont know what do to next I have sin and cosx's which i dont know what to do with

24. phi

write down what you have so far

25. Christians4

sinxcospi/4 +cpsxsinpi/4 / cospi/4cosx + sinpi/4sinx

26. phi

pi/4 is 45º it is good to have memorized cos(45) and sin(45)

27. Christians4

oh i knew that but can i convert it in the eqqn?

28. Christians4

so i could right 45deg instead of pi/4?

29. phi

30. phi

pi/4 and 45 mean the same thing.... it matters when using a calculator, or in certain math operations where radians are more useful... but the cos(45º) = cos(pi/4 radians)

31. phi

just like 1 foot is the same as 12 inches

32. Christians4

alright thanks

33. Christians4

I think i got it, gotta head to class now, ill ask teacher if hes free

34. Christians4