If A = 60∘ verify the following . tan2A=1−tan2A2tanA

tan2A=1−tan2A2tanAL.H.S=tan(2×60∘)=tan(180∘−60∘)=−tan60∘=−3 ......(1)R.H.S=1−tan2A2tanA=1−tan260∘2tan60∘=1−(3)223=1−323=−223=−3 ......(2)From (1) and (2)L.H.S=R.H.SHence verified

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If A = { 60 }^{ } verify the following . tan2A= { 2 tanA

Question

If A = $60^{\circ}$ verify the following .
$t an 2 A = \frac{2 t an A}{1 - t an ^{2} A}$

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If A =

60^{\circ}

verify the following .

t an 2 A = \frac{2 t an A}{1 - t an ^{2} A}

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Text solutionVerified

tan 2 A = \frac{2 tan A}{1 - tan ^{2} A}

L.H.S

= tan (2 \times 60^{\circ})

= tan (180^{\circ} - 60^{\circ})

= - tan 60^{\circ}

= - 3

......

(1)

R.H.S

= \frac{2 tan A}{1 - tan ^{2} A}

= \frac{2 tan 60 ^{\circ}}{1 - tan ^{2} 60 ^{\circ}}

= \frac{2 3}{1 - ( 3 ) ^{2}}

= \frac{2 3}{1 - 3}

= \frac{2 3}{- 2} = - 3

......

(2)

From

(1)

and

(2)

L.H.S

=

R.H.S

Hence verified

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Question Text	If A = $60^{\circ}$ verify the following . $t an 2 A = \frac{2 t an A}{1 - t an ^{2} A}$
Answer Type	Text solution:1
Upvotes	150

If A = 60∘ verify the following . tan2A=1−tan2A2tanA​

Text solutionVerified

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If A = $60^{\circ}$ verify the following .
$t an 2 A = \frac{2 t an A}{1 - t an ^{2} A}$