Math, asked by shivani77721, 4 months ago

if 2 sin 2 tita =root 3 the value of tita is​

Answers

Answered by Aryan0123
53

Solution:

\rm{2 \: sin2 \theta =  \sqrt{3} } \\  \\

Dividing by 2 on both sides,

\longrightarrow \:  \sf{sin2 \theta =  \dfrac{ \sqrt{3} }{2} } \\  \\

3/2 can also be written as sin 60°

\longrightarrow \:  \sf{sin \: 2 \theta = sin \: 60^{ \circ} } \\  \\

Taking sin inverse on both sides,

\longrightarrow \:  \sf{2 \theta =  {60}^{ \circ} } \\  \\

For finding the value of θ, divide both sides by 2.

\longrightarrow \:  \sf{ \theta =  \dfrac{60^{ \circ} }{2} } \\  \\

 \therefore \boxed{ \bf{ \theta =  {30}^{ \circ} }} \\  \\

Answered by TrustedAnswerer19
66

Step-by-step explanation:

Given,

 \:  \:  \:  \:  \:  \:  \:  \sf \:2 \: sin \: 2 \theta =  \sqrt{3}   \\  \sf \implies \: sin \: 2 \theta =  \frac{ \sqrt{3} }{2}  \\   \sf \implies \: 2 \theta =  {sin}^{ - 1} ( \frac{ \sqrt{3} }{2} ) \\   \sf \implies \: 2 \theta =  {60}^{ \circ}  \\  \sf \implies \:  \theta =  \frac{60}{2}  \\   \sf \therefore \:  \theta =  {30}^{ \circ}

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