Question

In a right angled triangle ABC , right angled at C, If tan A = √3 , then find

2 Sin B Cos A.
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Answer 1

$\underline{\boxed{\bold{Question}}}$  

↠ In a right angled triangle ABC , right angled at C, If tan A = √3 , then find  2 Sin B Cos A.

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$\underline{\boxed{\bold{Important\;Information}}}$  

↠ Trigonometric function is a unique relation between angles and side of triangle. Refer attachment for some special values of function assigned at certain degrees.  

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$\underline{\boxed{\bold{Given}}}$

↠ tan A = √3

↠ ∠C = 90°

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$\underline{\boxed{\bold{To\;Find}}}$

↠ Value of 2(sinB.cosA)

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$\underline{\boxed{\bold{Answer}}}$

Let's Start !

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Let's find value of angle A with given information.

$:\implies tanA = \sqrt{3}$

$:\implies tanA = \sqrt{3} = tan60^{\circ}$

$\boxed{:\implies A = 60^{\circ}}$

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So now let's find angle B.

By triangle sum property, Sum of all interior angles of triangle is 180°

$:\implies A + B + C = 180^{\circ}$

$:\implies 60^{\circ}+ B + 90^{\circ} = 180^{\circ}$

$\boxed{:\implies B = 30^{\circ}}$

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Now lets find value for our answer

$:\implies E = 2(sinB\times cosA )$

$:\implies E = 2(sin30^{\circ}\times cos60^{\circ} )$

$:\implies E = 2(\frac{1}{2} \times \frac{1}{2} )$

$\boxed{:\implies E = \frac{1}{2} }$

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$\boxed{\boxed{\bold{\therefore Value\;of\;E=2(sinB.cosA)\;= \frac{1}{2} }}}$

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Hope this helps u.../

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