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Question
If A =30o, then prove that :
sin 2A = 2sin A cos A = `(2 tan"A")/(1 + tan^2"A")`
Solution
Given A = 30°
sin 2A = sin 2(30°) = sin60° = `(sqrt3)/(2)`
2sin A cos A = 2sin 30° cos 30°
= `2(1/2)(sqrt3/2)`
= `(sqrt3)/(2)`
`(2 tan"A")/(1 + tan^2 30°) = (2tan 30°)/(1 + tan^2 30°)`
= `(2(1/sqrt3))/(1 + (1/sqrt3)^2`
= `(2/sqrt3)/(4/(3)`
= `(2)/(sqrt3) xx (3)/(4)`
= `(sqrt3)/(2)`
∴ sin 2A = 2sin A cos A = `(2tan"A")/(1 + tan^2 "A")`
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