What is the solution for 2-cos^2(35)-cos^2(55)=? with trigonometry

I know that for example sin(y) is
sin(90-x) = cos(x) if 90-x=y

1 Answer
Feb 26, 2018

#y=2-cos^2(35^@)-cos^2(55^@)=1#

Explanation:

We want to evalutae

#y=2-cos^2(35^@)-cos^2(55^@)#

We will use the trigonometric identities

  • #cos^2(x)=1/2(1+cos(2x))#

  • #cos(x)=-cos(180-x)#

Thus

#y=2-(1/2(1+cos(70^@)))-(1/2(1+cos(110^@)))#

#=2-(1/2+1/2cos(70^@))-(1/2+1/2cos(110^@))#

#=2-1/2-1/2cos(70^@)-1/2-1/2cos(110^@)#

#=1-1/2cos(70^@)-1/2cos(110^@)#

Use #cos(110^@)=-cos(180^@-110^@)=-cos(70^@)#

#y=1-1/2cos(70^@)-1/2(-cos(70^@))#

#=1-1/2cos(70^@)+1/2cos(70^@)#

#=1#