Question

Verify 4 csc 2x = 2 csc^2 x tanx
Help me please

Answer 1

@hartnn

Answer 2

lets take left side first.

4 csc 2x
convert csc x to sin x, know how ?

Answer 3

csc = 1/sin

Answer 4

how would I write that? The 4 and 2x are confusing me

Answer 5

now csc 2x = 1/ sin 2x

4 csc 2x
= 4/ sin 2x

you know the formula for sin 2x ?

Answer 6

No

Answer 7

sin 2x = 2 sin x cos x

plug this in

Answer 8

4/2 sin x cos x

Answer 9

ys, and 4/2 = 2

so for left side we have

2/(sin x cos x)

now we will try to simplify the right side, and check whether we get same expression.

2 csc^2 x tanx

convert both csc x and tan x in terms of sin x and cos x
can u

Answer 10

we would change csc^2 to cot^2 + 1?

Answer 11

since we know csc x = 1/sin x
try replacing
csc^2 x by 1/ sin^2 x

Answer 12

2/sin^2x

Answer 13

and what about that tan x ?

Answer 14

sin x/cos x

Answer 15

yes, so

what does that simplify to ?