Question

Prove the following identity.

Answer 1

sin(x) = cos (x-pi/2).
to prove it, use : http://library.thinkquest.org/20991/alg2...

(the equation is cos(x-y)=sin(x)sin(y)+cos(x)cos(y) )

so cos(x-pi/2) = cos(x) cos(pi/2) + sin(x) sin(pi/2)

and you know that cos(pi/2)=0 and sin(pi/2) = 1 so we get that sin(x) = cos (x-pi/2).

Now, plug in x+y instead of x in the equation we just proved to get cos(x + (y - pi/2)) = sin(x + y).

Answer 2

\[\frac{ 7\csc(t)-7 }{\cot(t)}=\frac{ 7\cot(t) }{ \csc(t)+1 }\]

Answer 3

@is3535 actually this ^^^ is what I want to prove

Answer 4

o srry

Answer 5

Factor out 7 in your numerator to get 7(cscx-1)/cotx

Answer 6

then multiply the numerator and the denominator by the conjugate of your numerator so that you can force an identity (Pythagorean Identity) into your proof so you can simplify

Answer 7

@quartzney I got 7(csc^2(t)-1), and got 7 cot (t) using a Pythagorean ID. I got the following:\[\frac{ 7\cot(t) }{ \cot(t)(\csc(t)+1)}\]

Answer 8

never mind. it's 7 cot^2(t)

Answer 9

ayyy glad u caught that

Answer 10

@quartzney I then expanded the cot^2(t) and got\[\frac{ 7\cot(t)\cot(t)}{ \cot(t)(\csc(t)+1) }\]

Answer 11

Then I cancelled one of the cot(t) s with the cot (t) on the bottom to finish the proof

Answer 12

perfect!

Answer 13

Ok. Thank you!!!!

Answer 14

you're very welcome!