Question

Simplify `cos60^@cos30^@+sin60^@sin30^@`?

Answer 1

`cos60^@cos30^@+sin60^@sin30^@=sqrt3/2`

Explanation:

Here we use the identity `cosAcosB+sinAsinB=cos(A-B)`

As we have `A=60^@` and `B=30^@`

`cos60^@cos30^@+sin60^@sin30^@`

= `cos(60^@-30^@)`

= `cos30^@`

= `sqrt3/2`