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Question
If A = 300 , verify that:
(i) sin 2A = `(2 tan A)/(1+tan^2A)`
Solution
A = 300
⇒ 2A = 2 × 300 = 600
(i) sin 2A = sin `60^0 = sqrt(3)/2`
`(2 tan A)/(1+tan^2A)= (2 tan 30^0)/(1+ tan ^2 30^0) = (2xx(1/sqrt(3)))/(1+(1/sqrt(3))^2`=`((2/sqrt(3)))/(1+1/3) =((2/sqrt(3)))/(4/3)=(2/sqrt(3)) xx 3/4=sqrt(3)/2`
∴ sin 2A = `(2 tan A)/(1+tan^2 A)`
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