Help with Trig Identities?

Question

I really need help understand Trigonometric Identities. Especially simplifying them in terms of sin and cos. Math is like a foreign language to me!! Could I get some tips on how to decipher this stuff?

Answer 1

You have to remember a figure given below positively
................................ +2,2
......................Hypota Opposite
............ alpha
0,0 +-----Adjacent----------+1,1

A triangle has been imagined . (+) 0,0 and (+) 1,1 and (+)2,2 are three vertexes of a triangle.

0,0,...1,1 is 'adjacent side' of angle alpha.
1,1...2,2 is opposite side of angle alpha
0,0...2,2 is hypotanuse(longest side) of Rt angle triangle!
(Opposite side and hypotanuse lines exists but not drawn)

Step-1 is to memorize above figure correctly.
Now remember only 3 letters "O, Aand H" that are short forms of "opposite, adjacent and hypotanuse"

Remember that...

O/H = Sin alpha
A/H = Cos alpha
O/A = Tan alpha
by any means of remembering. but a memory in relation to figure is ideal.

H/O = Cosec alpha---> 1/Sin
H/A = Sec alpha---> 1/ Cos
A/O = Cot alpha.---> 1/ Tan

Learn this at any cost, else you will not be able to use trignometry!

Please don't learn same things in diffrrent manners, Learn bare minimum basic relations and you will feel that applications are expanding from "a basic knowledge"!

Trignometry expands from 3 basic relations O/H, A/H and O/A which are Sin, Cos and Tan of a right angle triangle!

Answer 2

It's best that you memorize them. and ask for help.
"In mathematics, trigonometric identities are equalities that involve trigonometric functions that are true for all values of the occurring variables. These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common trick involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity."

Answer 3

learn secx,cosecx,tanx,cotx
sin(a+b), sin(a-b),
cos(a+b), cos(a-b),
sinx, cosx half formulas,
sin2x, cos2x, tan2x, ...