Question

verify: sinxtanx=secx-cosx

Answer 1

Have you considered changing everything to sine and cosine?

Answer 2

\[\large \sin x \tan x=\sec x-\cos x\]

So we want to leave one side as is, and try to manipulate the other side so they match.
That will effectively verify that they are equal.

So let's try manipulating the left side to match the right.
Do you understand what tkhunny was saying?
Let's rewrite the tangent in terms of sines and cosines.\[\large \sin x \color{orangered}{\tan x}=\sec x-\cos x\]\[\large \sin x \color{orangered}{\frac{\sin x}{\cos x}}=\sec x-\cos x\]

Following along so far?

Answer 3

ya. thats what i did but then i got sec^2x-1

Answer 4

For cos(x) NOT zero, we have \(sin^{2}(x) = 1 - \cos^{2}(x)\)

Answer 5

\[\sin x \tan x=\sin x { \sin x }/{ \cos x }=\sin x^{2}/\cos x=1-\cos x^{2}/\cos x=1/\cos x-\cos x^{2}/\cos x=\sec x-\cos x\]