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

Question

3647 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-25T10:28:01

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

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

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

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

= $cosBsinA-cosAsinB$

= $sinAcosB-cosAsinB$

= $sin(A-B)$

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

= $sin20^@$

How do you find the exact value of cos45sin65-cos65sin45cos45sin65-cos65sin45 using the sum and difference, double angle or half angle formulas?