Ex21 sin x pi4 cos x pi4 Ex22 sin x cos x 12Solution21 s

Ex21, sin (x + pi/4) = cos (x + pi/4) Ex22, sin x cos x = 1/2

21. sin ( x + pi/4)= cos(x + pi/4)

dividing both sides by cos(x+pi/4)

tan (x + pi/4)=1

Taking tan^^-1 both sides,we get

x+ pi/4= tan^-1(1)

x+pi/4= pi/4, 5pi/4

x=(pi/4 -pi/4), (5pi/4- pi/4)

x=0,pi in [0,360)

22. sinx cos x=1/2

mltiplying both sides by 2

2sinx cos x=1

sin 2x=1

taking sin^-1 both sides we get

2x= sin^-11

2x=pi/2,5pi/2

x=pi/4,5pi/4 in [0,2pi)