Question

"If 2 sin 2q = √3 than q=?​

Answer 1

GiveN :-

• 2 sin2Q = √3 .

To FinD :-

• The value of Q .

AnsweR :-

Given that , 2 sin 2Q = √3. Here 2Q is twice of angle Q .

⇒ 2 sin2Q = √3

⇒ sin2Q = √3/2

⇒ sin2Q = sin 60°

⇒ 2Q = 60°

⇒ Q = 1/2 ( 60° )

⇒ Q = 30° .

$\Large{\boxed{\pink{\sf Value\:of\:Q \;=\;30^{\circ}}}}$

___________________________________

★ KnowledgE Enhancer ★

Here , are the trignometric Ratios of some special angles :)

$\large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 65^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \csc & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}}$

Here are some more formulae of trigo :-

➳ $\sf\red{ cosec^2\theta - cot^2\theta=1}$

➳ $\sf\red{ sin^2\theta + cos^2\theta=1}$

➳ $\sf\red{ sec^2\theta - tan^2\theta=1}$

➳ $\sf\red{ sin(A+B)=sinA.cosB+cosA.sinB}$

➳ $\sf\red{ sin(A-B)=sinA.cosB-cosA.sinB}$

➳ $\sf\red{cos(A+B)=cosA.cosB-sinA.sinB }$

➳ $\sf\red{cos(A-B)=cosA.cosB+sinA.sinB }$

➳ $\sf\red{ tan(A+B)=\dfrac{tanA+tanB}{1-tanA.tanB}}$

➳ $\sf\red{ tan(A-B)=\dfrac{tanA-tanB}{1+tanA.tanB}}$

➳ $\sf\red{ tan(A+B+C)=\dfrac{tanA+tanB+tanC-tanA.tanB.tanC}{1-tanA.tanB-tanB.tanC-tanC.tanA}}$