Question

Show that 2tan30°/1tan30°=sin60°

Answer 1

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Q:-Show that 2tan30°/1tan30°=sin60°

$\huge\tt\underline\blue{Answer }$

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We Know that :-

$⟹tan30° = \frac{1}{ \sqrt{3} } </p><p>$

$⟹</p><p>sin60°30/// = \frac{ \sqrt{3} }{2}$

$⟹ \frac{2tan30°}{tan30°} = \frac{2 \times \frac{1}{ \sqrt{3} } }{ \frac{1}{ \sqrt{3} } } </p><p>$

$⟹ \frac{ \frac{2}{ \sqrt{3} } }{ \frac{1}{ \sqrt{3} } } = \frac{2 \sqrt{3} }{ \sqrt{3} } = 2</p><p>$

$⟹</p><p>tan60 = \frac{sin60°}{cos60°}$

$⟹ \frac{ \frac{ \sqrt{3} }{2} }{ \frac{1}{2} } = \frac{2 \sqrt{3} }{2} = \sqrt{3} </p><p>$

Not proved :-

✓Right Question:-2tan30/1+tan^230°

=2*1√3/1+(1/√3)^2

=2/√3/1+1/3

=2/√3/4/3

=2/√3*3/4

we can also write 3 as √3x√3

=2/√3*√3*√3/4

cancel one root 3 & 4 by 2 we get

=√3/2✓

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HOPE IT HELPS YOU..

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Answer 2

Q:-show that $\frac{2tan30}{1 + {tan}^{2}30 }$=sin60

$\huge\tt\underline\blue{Answer }$

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$\frac{2tan30}{1 + {tan}^{2}30 }$

$⟹ \frac{2 \times \frac{1}{ \sqrt{3} } }{1 + ( { \frac{1}{ \sqrt{3} }) }^{2} } </p><p>$

$⟹</p><p> \frac{ \frac{2}{ \sqrt{3} } }{1 + \frac{1}{3} }$

$⟹</p><p> \frac{ \frac{2}{ \sqrt{3} } }{ \frac{4}{3} } = \frac{2}{ \sqrt{3} } \times \frac{3}{4}$

$⟹ \frac{2}{ \sqrt{3} } \times \frac{ \sqrt{3} \times \sqrt{3} }{4} = \frac{2 \sqrt{3} }{4} = \frac{ \sqrt{3} }{2} </p><p>$

Hence proved

HOPE IT HELPS YOU..

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Thankyou:)