Question

what is value of a, if sin2 a= 2sin a​

Answer 1

Required Answer:-

Given:

• sin(2a) = 2sin(a)

To find:

• The value of a.

Solution:

Given that,

➡ sin(2a) = 2sin(a)

We know that,

➡ sin(2x) = 2sin(x)cos(x)

So,

➡ 2sin(a)cos(a) = 2sin(a)

➡ cos(a) = 1

From Trigonometry Ratio Table,

➡ cos(a) = cos(0°)

➡ a = 0°

Hence, the value of a is 0°

Trigonometry Ratio Table:

$\sf Trigonometry\: Value \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}$

Formula Used:

• sin(2x) = 2 sin(x) cos(x)