Question

Is Sec x tanx(1-sin^2x) = sinx a Identitie

Answer 1

Take any value of x and input into both sides of both sides give the same value thennyes it is a identity

Answer 2

Kind of makes sense ?

Answer 3

And yes it is and identity. You can prove it using trignometric identities

Answer 4

Okay Thanks!

Answer 5

Use the identity: \(\sin^2 x + \cos ^2 x = 1~~~ \rightarrow ~~~\cos^2 x = 1 - \sin^2 x\)\)

Also, \(\sec x = \dfrac{1}{\cos x}\), and \(\tan x = \dfrac{\sin x}{\cos x} \).


\(\sec x \tan x(1 - \sin^2 x) = \sin x\)

\(\dfrac{1}{\cos x} \times \dfrac{\sin x}{\cos x} \times \cos^2 x = \sin x\)

\(\dfrac{\sin x}{\cos^2 x} \times \cos^2 x = \sin x\)

\(\dfrac{\sin x}{\cancel{\cos^2 x}} \times \cancel{\cos^2 x} = \sin x\)

\(\sin x = \sin x\)

Answer 6

It is an identity.