Question #0bfd2

2 Answers
Jan 13, 2018

#1/2#

Explanation:

#sin^2theta+cos^2theta = 1# then

#1 = (sin^2theta+cos^2theta )^2=sin^4 theta+cos^4 theta+2 sin^2theta cos^2 theta# then

#sin^4 theta+cos^4 theta =1-2(sin theta cos theta)^2#

but if #sintheta-costheta=0 rArr sin^2theta+cos^2theta-2sinthetacostheta = 0#

then

#sinthetacostheta =1/2# and finally

#sin^4 theta+cos^4 theta =1-2(1/4) = 1/2#

Jan 13, 2018

Given

#sintheta-costheta=0#

#=>sintheta=costheta#

#=>sintheta/costheta=costheta/costheta#

#=>tantheta=1#

Now

#sin^4theta+cos^4theta #

#=cos^4theta+cos^4theta #

#=2cos^4theta #

#=2/sec^4theta #

#=2/(1+tan^2theta)^2 #

#=2/(1+1^2)^2 =2/4=1/2#