Question

If Sin2A = 2Sin A = 2Sin A than A is equal to (a) 0 (b) 2 (c) 1 (d) 3

Answer 1

given 
Sin 2A = 2 SinA
by double angle formula
2SinA CosA = 2 SinA
2SinA(CosA-1)=0
2 SinA =0 or CosA 1=0
SinA =0 or CosA=1
∴ SinA =0 

Answer 2

answer : option (a)

explanation : it is given that, sin2A = 2sinA.

we know, sin(A + B) = sinA.cosB + cosA.sinB

if A = B

then, sin(A + A) = sinA.cosA + sinA.cosA

or, sin2A = 2sinA.cosA use this application in above equation.

so, sin2A = 2sinA.cosA = 2sinA.

or, 2sinA.cosA - 2sinA = 0

or, 2sinA(cosA - 1) = 0

sinA = 0 and cosA = 1

for sinA = 0

A = 0, π, 2π, 3π, -π, -2π, ......

for cosA = 1

A = 0, 2π, 4π, 6π, -2π, -4π, .....

common values of A = 0, 2π, 4π, ...

in option (a), it is given that value of A = 0,

so, option (a) is correct choice.