Question

If Sin2A = 2SinA.Then find A

Answer 1

Answer:

The value of A is 0°

Solution:

Given,  

$\sin 2 A = 2 \sin A$

We know that the formula for sin 2A, i.e.,

$\sin 2 A = 2 \sin A \cos A$

Putting this in the above given expression, we get the following,

$\begin{array} { c } { 2 \sin A \cos A = 2 \sin A } \\\\ { 2 \sin A \cos A - 2 \sin A = 0 } \\\\ { 2 \sin A ( \cos A - 1 ) = 0 } \\\\ { ( \cos A - 1 ) = 0 } \end{array}$

Which gives sin A=0 or cos A = 1

$\begin{array} { c } { \cos A = 1 } \\\\ { A = \cos ^ { - 1 } 1 } \\\\ { A = 0 ^ { \circ } } \end{array}$

And

$\begin{array} { c } { 2 \sin A = 0 } \\\\ { \sin A = 0 } \\\\ { A = \sin ^ { - 1 } 0 } \\\\ { A = 0 ^ { \circ } } \end{array}$

Thus, the value of A will be 0° in both the cases.

Answer 2

Answer:

$Value \: of \: A = 0\degree$

Step-by-step explanation:

$Given \: sin2A=2sinA$

$\implies 2sinAcosA = 2sinA$

/* We know that,

sin2A = 2sinAcosA */

$\implies 2sinAcosA-2sinA=0$

$\implies 2sinA(cosA-1)=0$

$\implies 2sinA=0 \:Or \: cosA-1 = 0$

$\implies sinA=0 \:Or \: cosA = 1$

$\implies sinA=sin\:0\degree \:Or \: cosA = cos\:0\degree$

$\implies A = 0\degree$

Therefore,

$Value \: of \: A = 0\degree$

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