Question

if sin2A= 2sinA, what is the value of A?? is there any other way of solving this question without using sin2A formula?? ​

Answer 1

Answer:

Try complex no. I suppose

Step-by-step explanation:

Use Euler's Formula:

$re^{i\theta} = cos\theta + i.sin\theta\\\to sin\theta = \frac{e^{i\theta}-e^{-i\theta}}{2i}$

$sin2A = 2sinA\\\to \frac{e^{2Ai} - e^{-2Ai}}{2i} = 2 \frac{e^{Ai} - e^{-Ai}}{2i}$

Now cancel out the 2i term, and use formula of a^2 - b^2 =(a+b)(a-b)

${(e^{Ai} - e^{-Ai}) (e^{Ai} + e^{-Ai})} = 2{(e^{Ai} - e^{-Ai}) \\\to (e^{Ai} + e^{-Ai})} =2\\\to (e^{2Ai})^2 +1 = 2e^{Ai}\\\to (e^{Ai} -1)^2 =0\\\to e^{Ai} =1\\\to e^{Ai} =e^{(0 + 2n\pi))i}\\\to A = 0 +2n\pi$

Here n is any integer

You could also use Taylor series expansion here to find the ans. ..........[STAYHOME_STAYSAFE]