4.5 Prove Trigonometric Identities

I like this sub chapter the most!
This is because the answer has given and we are sure to get correct!
Let's check it out!

In this section, we have to prove other identities by using trigonometric identities.
There are several identities which are:

Pythagorean Identities

sin^2 x + cos^2 x = 1
1+cot^2 x = cosec^2 x
1+tan^2 x = sec^2 x


Quotient Identity

tan x = sin x /cos x


Reciprocal Identities

cosec x = 1 / sin x
sec x = 1 / cos x
cot x = 1 / tan x =  cos x / sin x


Compound Angle Formulas

sin (x+y) = sin x cos y + cos x sin y
sin (x-y) = sin x cos y - cos x sin y

cos (x+y) = cos x sin y - sin x sin y

cos (x-y) = cos x sin y + sin x sin y

sin2x = 2sin x cos x
cos2x = cos^2 x -sin^2 x
           = 1 - 2sin^2 x
           = 2cos^2 x -1
tan2x = 2tan x / 1 - tan^2 x

Strategy that we need to 'survive' in proving are as below:

1. Perform substitution is based on established identities

2.Employalgebraic Manipulations:

   - factoring

   - creating common

   - denominator

             &

Lastly and it is very important

3. Common sense!!

If you are still confusing on this sub chapter

Here are videos which show how to prove of some examples

Check it out and have fun! 

* Always remember that prove the identities by starting from complicated side !! :)