Question

Taking A=60° ,Prove the question sin2A = 2sinA .cosA​

Answer 1

Answer:

Proven

Step-by-step explanation:

Given: A=60°

To Prove: sin2A = 2sinAcosA

RHS = 2sinAcosA

⇒ 2sin60°cos60°

⇒ 2(√3/2)(1/2)                                                 [ sin60° = √3/2   cos60°= 1/2 ]

⇒ √3/2 = sin60° = sin120°                                       [ sin(180-A) = sinA ]

⇒ sin2*60° = sin2A = LHS

Hence Proved!

Answer 2

Step-by-step explanation:

To prove : sin2A= 2sinA.cosA

Proof : let A=60

$\sin(2 \times 60) = 2 \sin(60) \times \cos(60)$

$\sin(120) = 2 \sin(60) \times \cos(60)$

$\sin(90 + 30) = 2 \sin(60) \times \cos(60)$

$\cos(30) = 2 \sin(60) \times \cos(60)$

$\frac{ \sqrt{3} }{2} = 2 \times \frac{ \sqrt{3} }{2} \times \frac{1}{2}$

$1 = 1$

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