Cos(x)=sin(x). Then the value of cos^4x + sin^4x=?

1 Answer
May 14, 2018

#1/2#

Explanation:

#Cos(x)=sin(x)#

Usually I avoid dividing by #sinx# or #cosx# because I lose solutions, but we will try solving the equation both ways to see if we get the same solution and all solutions are included:
Divide by #sinx# on both sides:
#cotx=1#
#x=pi/4, (5pi)/4#
#x=pi/4+pin#

Divide by #cosx# on both sides:
#tanx=1#
#x=pi/4, (5pi)/4#
#x=pi/4+pin#

Yields the same solution either way so:
#(+-sqrt2/2)^4 + (+-sqrt2/2)^4=#

#1/4+1/4=1/2#