If is in quadrant II and cos 23 find sin 2 and cos 2Soluti

If is in quadrant II and cos = 2/3 , find sin 2 and cos 2.

Solution

is in quadrant II and cos = 2/3 ,

find sin = sqrt( 1 - cos^2) ( sin is +ve in QII )

= sqrt( 1 -(-2/3)^2 ) = sqrt(5)/3

find sin 2 and cos 2

sin2 = 2sincos = 2(sqrt(5)/3)(-2/3)

= -4sqrt(5)/9

cos2 = 2cos^2 - 1

= 2(-2/3)^2 -1

= 8/9 -1

= -1/9