Question

given A=30°,verify Sin 2A =2 Sin A Cos A .plzz give answer in detail ​

Answer 1

Answer:

LHS = SIN 2A

=SIN 60⁰

=

$\sqrt{3} \div 2$

RHS= 2 SIN A COS A

=2 SIN 30⁰ COS 30⁰

$= 2 \times </u></em></strong><strong><em><u>(</u></em></strong><strong><em><u>1 \div 2</u></em></strong><strong><em><u>)</u></em></strong><strong><em><u> \times </u></em></strong><strong><em><u>(</u></em></strong><strong><em><u> \sqrt{3} \div 2</u></em></strong><strong><em><u>)</u></em></strong><strong><em><u>$

$= \sqrt{3} \div 2$

SINCE LHS=RHS

SUM IS PROVEN

FOLLOW ME

MARK AS BRAINLIEST

Answer 2

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given : }} \\ \tt: \implies \angle \: A = 30 \degree \\ \\ \red{\underline \bold{To \: Verify: }} \\ \tt: \implies sin \: 2A = 2 \: sin A \: cos \: A$

• According to given question :

$\tt \circ \: sin \: 2A = 2 \: sin \: A\: cos \: A \\ \\ \bold{Solving \: L.H.S : } \\ \tt: \implies sin \: 2A= sin \: 2 \times 30 \degree \\ \\ \tt: \implies sin \: 2A = sin \:60 \degree \\ \\ \green{\tt: \implies sin \: 2A = \frac{ \sqrt{3} }{2} } \\ \\ \bold{Solving \: R.H.S : } \\ \tt: \implies 2 \: sin \: A \: cos \:A = 2 \: sin \: 30 \degree \times cos \: 30 \degree \\ \\ \tt: \implies 2 \: sin \: A \: cos \: A = 2 \times \frac{1}{2} \times \frac{ \sqrt{3} }{2} \\ \\ \green{\tt: \implies 2 \: sin \: A \: cos \: A = \frac{ \sqrt{3} }{2} } \\ \\ \green{\tt \therefore L.H.S = R.H.S} \\ \\ \red{\huge{\bold{verified }}}$