Question #d55d1

3 Answers
Nov 16, 2017

#x=(2n+1)(*pi/4)# where #ntoZZ#

Explanation:

#cos^2x-sin^2x=0#

or, #cos2x=0#

or, #2x=(2n+1)*(pi/2)#

or, #x=(2n+1)(*pi/4)# where #ntoZZ#

Nov 16, 2017

#x=n360^circ+-45^circ or 2npi+-pi/4, ninZZ#

Explanation:

The double angle formula gives us #cos(2A)=cos^2A-sin^2A#

Using this, we know that #cos(2x)=0#

#2x=arccos(0)=90^circ or pi/2#

#x=45^circ or pi/4#

However, #x=n360^circ+-45^circ or 2npi+-pi/4, ninZZ##

Nov 16, 2017

x = 45 degree

Explanation:

We know #cos^2 x + sin^2 x = 1. or, cos^2 x = 1 - sin^2 x#

Put the value of #cos^ 2 x #, in #cos^2 x - sin^2 x = 0# we get,

#rArr 1 - sin^2 x - sin^2 x = 0#

#rArr -2sin^2 x = -1#

#rArr sin^2 x = 1/2#

#rArr sin x = sqrt (1/2) = sin 45^*#

#rArr x = 45^*#