Question

tan theta =1√3 find the value of sin theta *cos theta​

Answer 1

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Answer 2

$\huge\tt{\red{GIVEN:}}$

★$tan\theta=\dfrac{1}{\sqrt{3}}$

$\huge\tt{\red{TO\:FIND:}}$

★$sin\theta \times cos\theta$

$\huge\tt{\red{:ANSWER:}}$

We have,

=>$tan\theta =\dfrac{1}{\sqrt{3}}$

=>$tan\theta = tan30°$

$\large\green{\boxed{tan30°=\dfrac{1}{\sqrt{3}}}}$

Eliminating tan both sides,

.°. $\theta = 30°$

______________________________________

Now,

We have to find $sin\theta×cos\theta$

= $sin30° × cos30°$

=$\dfrac{1}{2}×\dfrac{\sqrt{3}}{2}$

$\large\purple{\boxed{sin30°=\dfrac{1}{2},\:cos30°=\dfrac{\sqrt{3}}{2}}}$

=$\dfrac{\sqrt{3}}{4}$

$\huge\orange{\boxed{sin\theta\times cos\theta= \dfrac{\sqrt{3}}{4}}}$