Question

2sin 2a =√3 find the value
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Answer 1

Question :–

▪︎ Find General solution of following equation –

$\implies { \bold{2 \: sin(2a) = \sqrt{3} }}$

Answer :–

$\\ \implies { \bold{2 \: sin(2a) = \sqrt{3} }}$

$\\ \implies { \bold{ \: sin(2a) = \dfrac{ \sqrt{ 3} }{2} }}$

▪︎ We should write this as –

$\\ \implies { \bold{ \: sin(2a) = sin( \frac{\pi}{3}) }}$

▪︎ We know that if ${ \bold{ \: sin( \theta) = sin( \alpha ) }}$ then –

$\\ \longrightarrow { \red { \boxed{ \bold{ \: \theta = n\pi + {( - 1)}^{n} \alpha \: \: , \: \: n \in \: z}}}}$

▪︎ So that –

$\\ \implies { \bold{ \: 2a = n\pi + {( - 1)}^{n} ( \frac{\pi}{3} ) }}$

$\\ \implies { \boxed{ \bold{ \: a = \dfrac{n\pi}{2} + {( - 1)}^{n} ( \frac{\pi}{6} )}}}$

EXTRA INFORMATION :–

▪︎ If ${ \bold{ \: sin( \theta) = sin( \alpha ) }}$ then –

$\\ \longrightarrow { \red { \boxed{ \bold{ \: \theta = n\pi + {( - 1)}^{n} \alpha \: \: , \: \: n \in \: z}}}}$

▪︎ If ${ \bold{ \: cos( \theta) = cos( \alpha ) }}$ then –

$\\ \longrightarrow { \red { \boxed{ \bold{ \: \theta =2 n\pi \pm \alpha \: \: , \: \: n \in \: z}}}}$

▪︎ If ${ \bold{ \: tan( \theta) = tan( \alpha ) }}$ then –

$\\ \longrightarrow { \red { \boxed{ \bold{ \: \theta = n\pi + \alpha \: \: , \: \: n \in \: z}}}}$