Question

Hey guys , i'm new to this site and i have three math questions that i need help with.
1. tan2x = 2tanx/sec^2x-2tan^2

2.sec(x)csc^2(x)-csc^2(x) = sec(x)/1+cos(x)

3.cos(x)sin(x)/1+cos = cos(x)-cos^2x

The problems are all "prove the identities" .
I am in major need of help , thank you!

Answer 1

1. \[\frac{ 2\tan x }{\sec ^{2}x-2\tan ^{2}x }=\frac{ 2\tan x }{\sec ^{2}x-\tan ^{2}x-\tan ^{2}x }=\frac{ 2\tan x }{ 1-\tan ^{2}x} =\tan 2x\]

Answer 2

2.
\[\frac{ \sec x }{1+\cos x }*\frac{ 1-\cos x }{ 1-\cos x }=\frac{\sec x \left( 1-\cos x \right) }{1-\cos ^{2}x }\]
\[=\frac{ \sec x \left( 1-\cos x \right) }{\sin ^{2}x }=\frac{ \sec x-1 }{\sin ^{2}x }=\sec x \csc ^{2}x-\csc ^{2}x\]

Answer 3

check the statement of 3rd.