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Question
prove that:
sin (2 × 30°) = `(2 tan 30°)/(1+tan^2 30°)`
Solution
RHS = `(2 tan 30°)/(1+tan^2 30°) = (2xx1/(sqrt3))/(1 +(1/sqrt3)^2) = (2/(sqrt3))/(1+(1)/(3)) = (2/sqrt3)/(4/(3)) =2/sqrt3xx3/4=3/(2sqrt3)xxsqrt3/sqrt3=(3sqrt3)/(2xx3)= (sqrt3)/(2)`
LHS = sin (2 × 30°) = sin 60° = `(sqrt3)/(2)`
∴ LHS = RHS
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