Question

Prove that : `"sin"(pi)/(3) "tan"(pi)/(6) +"sin"(pi)/(2) "cos"(pi)/(3) =2 "sin"^(2)(pi)/(4)`.

Answer 1

`LHS="sin"(pi)/(3) "tan"(pi)/(6) +"sin"(pi)/(2) "cos"(pi)/(3)`
`=sin60^(@) tan30^(@)+sin90^(@) cos60^(@)`
`=(sqrt(3))/(2) xx (1)/(sqrt(3)) + 1xx(1)/(2)=(1)/(2)+(1)/(2)=1`
`RHS=2 "sin"^(2)(pi)/(4) =2xx((1)/(sqrt(2)))^(2)=2xx(1)/(2)=1.`
`therefore LHS=RHS.` [Proved]