SOLUTION: simplify the expression: cscx(tan(-x)) simplify the expression: cotxcos(3.14/2-x) verify the identity: cos^4x-sin^4x=cos^2x-sin^2x

Algebra ->  Trigonometry-basics -> SOLUTION: simplify the expression: cscx(tan(-x)) simplify the expression: cotxcos(3.14/2-x) verify the identity: cos^4x-sin^4x=cos^2x-sin^2x       Log On


   

Question 82694: simplify the expression: cscx(tan(-x))
simplify the expression: cotxcos(3.14/2-x)
verify the identity: cos^4x-sin^4x=cos^2x-sin^2x
Found 2 solutions by kev82, funmath:
Answer by kev82(151) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,

i'm very sorry if I'm wrong, but I get the impression you just want the answers, so I'm going to give some helpful advice instead. If you have tried it then please post where you're stuck.

First question: For questions like this, I always recommend you go back to basics. Replace everything in terms of sine and cosine. Well, cosec=1/sin and tan=sin/cos. (You need to remember these!) I'm sure you can take it from there. Don't forget what sin(-x) and cos(-x) are.

Second Question: The idea is the same as last time, write everything in terms of sines and cosines. If you don't know cot=cos/sin. However this time we need to get rid of that pi/2. See what you can do with the addition formula for cosine (you should also know this) .

Third Question: I'm sure there are many ways to do this. My method is to write everything in terms of cos(2x). What do you get if you let A=B in the addition formula given above for cosine. can you combine this with the identity to get as a function of . let me know how you get on with this one because it's quite hard. If you get stuck post back with your working.

Hope that helps,
Kev

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
simplify the expression: cscx(tan(-x))
%281%2F%28sinx%29%29%2A%28%28sin%28-x%29%29%2F%28cos%28-x%29%29%29 Reciprocal identity
%281%2F%28sinx%29%29%2A%28%28-sinx%29%2F%28cosx%29%29 even an odd property
-1%2F%28cosx%29 cancel sinx
-secx reciprocal identity
:
simplify the expression: cotxcos(3.14/2-x)
cotx%2Acos%28pi%2F2-x%29
cotx%2Asinx complementary angles
%28%28cosx%29%2F%28sinx%29%29%2Asinx reciprocal identity
cosx cancel sinx
:
verify the identity: cos^4x-sin^4x=cos^2x-sin^2x
%28cos%5E2%28x%29%2Bsin%5E2%28x%29%29%28cos%5E2%28x%29-sin%5E2%28x%29%29 factoring the difference of perfect squares
1%28cos%5E2%28x%29-sin%5E2%28x%29%29 pythagorean identity
cos%5E2%28x%29-sin%5E2%28x%29=cos%5E2%28x%29-sin%5E2%28x%29
:
These can actually be pretty fun once you've memorized all your identitities. They're like puzzles. Attack the more complicated side and simplify, it's much easier to break it down than to try to figure out how to build the simpler side into something more complicated.
Happy Calculating!!!!