Question

PLEASE HELP ME!!!!!!!!!!
prove the identity step by step with its rule
cos(3pi/2-x)/cos(pi+x)=tanx

Answer 1

you can use cos(a-b) = cos(a)cos(b) + sin(a)sin(b

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

Answer 2

Okay so\[\cos(\frac{ 3 \pi }{ 2 }-x)=\cos(\frac{ 3\pi }{ 2 })\cos(x)+\sin(\frac{ 3\pi }{ 2 })\sin(x)\]

I just used cos(a - b)

Answer 3

Now:\[\cos(\pi+x)=\cos(\pi)\cos(x)-\sin(\pi)\sin(x)\]

Answer 4

Now plug those back into the expression:\[\frac{ \cos(\frac{ 3\pi }{ 2 })\cos(x)+\sin(\frac{ 3\pi }{ 2 })\sin(x) }{ \cos(\pi)\cos(x) - \sin(\pi)\sin(x) }\]

cos(pi) = -1
sin(pi) = 0
cos(3pi/2) = 0
sin(3pi/2) = -1

Taking this into account the expression simplifies to:\[\frac{ \sin(x) }{ \cos(x) }\]

which is tan(x)

Answer 5

it actually equals -tan(x)

Answer 6

so was ur question asking tan(x) or -tan(x) ?