Proving Trigonometric Identities

[mathnewb]

Homework Statement

1) sin(x+y)sin(x-y)=cos^2y-cos^2x

2) tan(∏⁄4+x)+tan(∏/4-x)=2sec2x

3) cosx-cosy=-2sin(x+y/2)sin(x+y/2)

4) 2cotx-2tanx=4-2sec^2x/tanx

Homework Equations

all trig identities

The Attempt at a Solution

1) i understand that i should show what i have attempted but there is way too many lines of manipulating the equations and i don't have the time to write it down. i can say that for all of these identities i have changed them to cos and sin as these can be the easiest to solve and then used trig identities to make both sides look the same. i have nt had any luck with these and i was hoping you guys could help me

thx alot!

 

[yeongil]

3) cosx-cosy=-2sin(x+y/2)sin(x+y/2)

Is it (x+y)/2 or x+(y/2)?

4) 2cotx-2tanx=4-2sec^2x/tanx

Again... is it (4-2sec^2x)/tanx or 4-(2sec^2x/tanx)?

1) i understand that i should show what i have attempted but there is way too many lines of manipulating the equations and i don't have the time to write it down. i can say that for all of these identities i have changed them to cos and sin as these can be the easiest to solve and then used trig identities to make both sides look the same. i have nt had any luck with these and i was hoping you guys could help me

Sorry, you'll have to make time to write what you have so far if you want us to help. I'll give you one suggestion -- in #2, don't convert to cosines and sines as your first step. Too messy. Instead, use the tangent sum & difference formulas.01