Question

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

Answer 1

`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`