Question

How do you use the sum and difference formula to simplify `sin40cos10+sin40sin10`?

Answer 1

`sin40^ocos10^o +cos40^osin10^o=sin50^0`

Explanation:

I think the question should be `sin40^ocos10^o +cos40^osin10^o` and not** `sin40^ocos10^o +sin40^osin10^o`

Sum formula for sine function is

`sin(A+B)=sinAcosB+cosAsinB`

Here we have `sin40^ocos10^o +cos40^osin10^o`

it is evident comparing above two that

`sin40^ocos10^o +cos40^osin10^o=sin(40^0+10^0)=sin50^0`