how do I solve Tan X cos X?

Question

Write each expression in terms of sines and/or cosines, and then simplify.

1. Tan x cos X
2. sec X cos X
3. Sin x cot x
4. sin x csc x
5. sec x/tan x
6.cot x/csc x

I have no idea how to do this....

Answer 1

1. Tan x cos X

2. sec X cos X

3. Sin x cot x

4. sin x csc x

5. sec x/tan x

6.cot x/csc x



OK

Tan = Sine/Cosine

So, in #1, Tan x Cos x = (Sine/Cosine) times Cosine

The cosines cancel and the answer is Sine x



You can do the others if I tell you that

Cosec = 1/Sine

Sec = 1/Cosine

Cot = 1/Tan = Cosine/Sine



Hope this helps. Let me know if you need more help. I'm on YM or by email.

Best of luck.

Answer 2

for this you need to use trig identities you can look them up on the internet. it would be a good idea to look them up and write them down. i have the answers below if you want to se the work explained thats at the bottom.

1. sinx

2. 1

3. cosx

4. 1

5. 1/sinx

6. cosx



1. tanx=sinx/cosx

therefore: tanxcosx=(sinx/cosx)cosx

cosines cancel out leaving just sinx



2.secx=1/cosx

therefore: secxcosx=(1/cosx)cosx

again, cosines cancel leaving 1



3. cotx=cosx/sinx

therefore: sinxcotx=sinx(cosx/sinx)

sines cancel leaving cox



4. cscx=1/sinx

therefore: sinxcscx=sinx(1/sinx)

sines cancel and leave 1



5. secx=1/cosx and tan=sinx/cosx

therefore: secx/tanx= (1/cosx)/(sinx/cosx)

multiply the top fraction by the reciprocal of the bottom or multiply 1/cosx by cosx/sinx

cosines cancel leaving 1/sinx



6. cotx=cosx/sinx and csc= 1/sinx

therefore: cotx/cscx=(cosx/sinx)/(1/sinx)

same as above multiply (cosx/sinx)by(sinx/1)

sines cancel leaving cosx

Answer 3

tan x = sinx/cosx



so:



tanx cosx = (sinx/cosx)cosx = sinxcosx/cosx = sinx



Sec x = 1/cosx so secx cosx = cosx/cosx = 1



cot x = 1/tan x = cosx/sinx

Thus sinx cotx = sinx(cosx/sinx) = sinxcosx/sinx = cos x



csc x = 1/sin x

thus sinx csc x = sinx/sinx = 1



secx = 1/cosx and tan x = sinx/cosx

thus sec x/tanx = (1/cosx)/(sinx/cosx) = (1/cosx)(cosx/sinx) =1/sinx

= csc x



cotx/cscx = cosx/sinx / 1/sinx = cosx/sinx * sinx = cos x

Answer 4

someone hasnt been paying attention in class!

but if you really want help add me on skype..i can do every one of them- lazim.sharar