Page 9 - Trigonometry

Example 2:

1. Prove that

sin(4 )
4 sin( ) cos( ) =
cos(2 )
Use the identities,

sin(2 ) = 2 sin( ) cos( )

sin(4 ) = 2 sin(2 ) cos(2 )

4 sin( ) cos( ) = 2sin(2 )

sin(4 )
2 sin(2 ) =
cos(2 )

which completes the identity.

2. Find the value of x (0 ≤ ≤ 2 ) which satisfies the

condition

sin( ) + sin ( ) = 0
2

Use the identity,

sin( ) = 2 sin ( ) cos ( )
2 2
therefore

2 sin ( ) cos ( ) + sin ( ) = 0
2 2 2

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