Trig Identities im having trouble with this trig identity?

Question

Hi, im having some touble with this trig question and was just wondering if i could get some help with it, any help would be great the question is
prove: sinx-tanx = sinxtanx

~ Thnx

Hi, im having some touble with this trig question and was just wondering if i could get some help with it, any help would be great the question is
prove: sinx-tanx = -sinxtanx

sry i forgotte the - after the = sign last time
~ Thnx

SORRY one more fix i actually got the equation from a friend and he forgotte to tell me that everything was ^2 im still not sure 100% if this will be an identity but from what i know this should be an identity

sin^2x - tan^2 x = -sin^2x tan^2 x

Answer 1

sin^2x - tan^2x
sin^2x - (sin^2x/cos^2x).....because tanx = sinx/cosx
(cos^2x sin^2x - sin^2x)/cos^2x
sin^2x(cos^2x - 1)/cos^2x
-sin^2x(1 - cos^2x)/cos^2x
-sin^2x(sin^2x)/cos^2x.....because sin^2x + cos^2x = 1
-tan^2x * sin^2x.....because tanx = sinx/cosx

Whoo hoo, I see I'm the first one to have checked back to find the right "identity" to prove. :-)

Answer 2

sinx-tanx = sinxtanx
sinx -sinx/cosx = sinx *sinx /cosx
sinxcosx - sinx = sin^2x
cosx -1 = sinx
The above is not true so your original expression is not an identity. That's why you are having trouble proving that it is.

Answer 3

Hi Maddie 1 - cos x / sin x mutiply and divide by 1+cosx = (1-cos x)(1+cos x) / sin x(1+cos x) = (1-cos2 x)/sin x(1+cos x) = (sin2 x)/sin x (1 + cos x) = sin x / 1 + cos x LHS = RHS Shy

Answer 4

It ia not an identity.
LHS and RHS are equal only when x = 0 or kpi where k is any integer.

Answer 5

sin x - tan x = sin x tan x
(sin x cos x) / cos x - sin x / cos x = sin x tan x
sin x (cos x - 1) / cos x = sin x tan x
(tan x)(cos x - 1) = sin x tan x

Since this is not true, we cannot prove the identity.

Answer 6

Correct your question please.