Sine of sum and difference with 3 values

[afrocod]

Homework Statement

<sub>sin (90 - θ + λ)

= sin90cos(θ + λ) - cos90sin(θ + λ)

= cos(θ + λ)

The book says cos(θ - λ)

So are we both right and if so how can I manipulate mine to look like the books answer.</sub>

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

hi afrocod!

sin (90 - θ + λ)

= sin90cos(θ + λ) - cos90sin(θ + λ)

no, sin (90 - θ + λ) = sin (90 - (θ - λ))

= sin90cos(θ - λ) - cos90sin(θ - λ)

 

[afrocod]

Ah my old friend Tim.

I was surprised that 100's of people looked at this and nobody answered. I suspected this was a super easy question, as you just proved.

Thank you very much.