Question

Use trigonometric identities to transform the left side of the equation into the right side (0 < θ < π/2).
sin2 θ − cos2 θ=sin2 θ − (?????)
= 2 sin2 θ − 1

Answer 1

well

\[\sin^2 + \cos^2 = 1\]

rewrite this equation

\[\cos^2 (x) = 1- \sin^2(x)\]

substitute into the original equation

\[\sin^2(x) - (1 - \sin^2(x) = 2\sin^2(x) - 1\]

Answer 2

i just need to know what to put in the ???? part. this is confusing me. i understand what you mean though.

Answer 3

Just looking at it (no calculation, formula or anything) if you put (1-sin2 theta) then you get the last line.

Answer 4

then you need to solve

2sin^2(x) = 1

sin^2x = 1/2

and \[\sin(x) = \pm \frac {1}{\sqrt{2}}\]

Answer 5

1st quadrant as 0<x<pi/2

then x = pi/4

Answer 6

The questioner is not actually asking for anything to be solved.....

Answer 7

I substituted 1 - sin^2(x) for cos^2(x)