Prove a trigonometry equation

[Jackie01]

Prove left hand side equals right hand side. sin 2x + 2sin^2(45-x) = 1 I would really appreciate any help! I am struggling to do this.

 

[DrPhil]

Prove left hand side equals right hand side. sin 2x + 2sin^2(45-x) = 1 I would really appreciate any help! I am struggling to do this.

We need to see your work to see where you are stuck!

Start by replacing sin(2x) using the double angle (or sum x+x) formula.
Use the sum (difference) formula for sin(45° - x), and square it.
See what happens next!

 

[Deleted member 4993]

Prove left hand side equals right hand side. sin 2x + 2sin^2(45-x) = 1 I would really appreciate any help! I am struggling to do this.

Hint:

1 - 2sin²(Θ) = cos(2Θ)

 

[HallsofIvy]

Is the "45" in "45- x" in degrees?

 

[Jackie01]

We need to see your work to see where you are stuck!

Start by replacing sin(2x) using the double angle (or sum x+x) formula.
Use the sum (difference) formula for sin(45° - x), and square it.
See what happens next!

Thanks so much ..i finally got it after many attempts lol

 

[Deleted member 4993]

sin 2x + 2sin²(45-x)

= sin(2x) - [1 - 2sin²(45-x)] +1

= sin(2x) - cos{2*(45-x)} +1

= sin(2x) - cos(90-2x) +1

= sin(2x) - sin(2x) +1

= 1