Prove the following identity tan x cos x/sin x=1/sin x cos x
tan x cos x/sin x=1/sin x cos x
or
tan x cos x/sin x=1/(sin x cos x) ?
For either case,
LS = tanx(cosx/sinx)
= tanx cotx
= 1
For any given x, RS ≠ 1
Your equation is NOT an identity, so it cannot be proven to be true.
Its tan x cos x/sin x=1/sin x cos x
yup, that's what you typed the first time.
And I pointed out to you that that is not an identity.
To prove the given trigonometric identity:
tan(x) * cos(x) / sin(x) = 1 / (sin(x) * cos(x))
We will start with the left-hand side (LHS) and manipulate it step by step until we reach the right-hand side (RHS):
LHS: tan(x) * cos(x) / sin(x)
Step 1: Rewrite tan(x) as sin(x) / cos(x)
LHS: (sin(x) / cos(x)) * cos(x) / sin(x)
Step 2: Cancel out the common terms sin(x) and cos(x)
LHS: 1
Hence, we've proved that the LHS equals 1. Therefore, the given identity is true.