Question

How do you find the exact value of `cos45sin65-cos65sin45` using the sum and difference, double angle or half angle formulas?

Answer 1

`cos45^@sin65^@-cos65^@sin45^@=sin20^@`

Explanation:

We use the difference identity `sin(A-B)=sinAcosB-cosAsinB`

Here let us use `A=65^@` and `B=45^@`

Hence `cos45^@sin65^@-cos65^@sin45^@`

= `cosBsinA-cosAsinB`

= `sinAcosB-cosAsinB`

= `sin(A-B)`

= `sin(65^@-45^@)`

= `sin20^@`