Question

$\sqrt{3} tan \: theta = 1then \: find \: the \: value \: of \: 2sin \: teta \: costheta$
plss its urgent ​

Answer 1

Step-by-step explanation:

Given{⇝2sin2θ=3

{\huge{\red{\sf{To\:Find}}}}\begin{cases}\leadsto \bf{The\:value\:of\:\theta}\end{cases}ToFind{⇝Thevalueofθ

\huge\red{\underline{\bf{\green{Answer:}}}}Answer:

{\underline{\pink{\sf{\hookrightarrow Taking\:the\: given\: equation:}}}}↪Takingthegivenequation:

\sf{\implies 2\sin 2\theta =\sqrt{3}}⟹2sin2θ=3

\sf{\implies \sin 2\theta=\dfrac{\sqrt{3}}{2}}⟹sin2θ=23

\sf{\implies \sin 2\theta=\sin 60^{\circ}}⟹sin2θ=sin60∘

\purple{\sf{Comparing\: both \:sides ,}}Comparingbothsides,

\sf{\implies 2\theta = 60^{\circ}}⟹2θ=60∘

\sf{\implies \theta =\dfrac{60^{\circ}}{2}}⟹θ=260∘

{\underline{\boxed{\red{\bf{\longmapsto \theta =30^{\circ}}}}}}⟼θ=30∘

{\underline{\underline{\orange{\sf{\leadsto Hence \:the\:value\:of\:\theta\:is\:30^{\circ}}}}}}⇝Hencethevalueofθis30∘

\rule{200}5

Some more values of sine:

sin0° = 0.

sin 30° = ½.

sin 45° = 1/√2.

sin 60° = √3/2.

sin 90° = 1

Answer 2

Answer:

$tan\theta=\frac{1}{\sqrt{3} } \\\theta=30\\2sin\theta\cos\theta=2sin30cos30=2\times\frac{1}{2}\times\frac{\sqrt{3} }{2}= \frac{\sqrt{3} }{2}$