To verify the given identity, we work with the value on the right hand side. That is:
2 (csc^2 (x)) (tan x)
We know that csc is the inverse of sine and that tan = sin / tan, therefore:
= 2 (1 / sin^2 (x)) (sin x / cos x)
Cancelling sin x:
= 2 (1 / sin x) (1 / cos x)
Multiplying both the numerator and denominator by 2:
= 4 / 2 sin x cos x
From the trigonometric identities, 2 sin x cos x = sin 2x, therefore:
= 4 / sin 2x
= 4 csc 2x
Hence, it is proven.
Answer:
Step-by-step explanation:
work on the right hand side.
csc is the inverse of sin and tan equals sin/cos which gives us:
2(1/((sin^2)x))((sinx)/(cosx))
next cancel sinx which gives us:
2(1/(sinx))(1/(cosx))
then we multiply the numerator and denominator by 2:
4/((2sinx)(cosx))
simplify using identities:
4/2sinx
simplify using identities:
4csc2x
