Question

4. Find the value of tan9°tan27°tan60°tan63°tan81° (2)
1) √2
2) 3
3) √3​

Answer 1

Answer:

√3 is your answer

Step-by-step explanation:

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Answer 2

TO FIND :–

• Value of tan(9°)tan(27°)tan(60°)tan(63°)tan(81°) = ?

SOLUTION:–

▪︎ Let suppose that –

$\\ \implies \sf y = \tan( {9}^{ \circ} ) \tan( {27}^{ \circ}) \tan( {60}^{ \circ} ) \tan( {63}^{ \circ}) \tan( {81}^{ \circ} )$

• We know that –

$\\ \sf \dashrightarrow \tan( \theta) = \cot( {90}^{ \circ} - \theta)$

$\\ \implies \sf y = { \underbrace{ \sf \: \tan( {9}^{ \circ} ) \tan( {81}^{ \circ})}} \tan( {60}^{ \circ} ){ \underbrace{ \sf \tan( {63}^{ \circ}) \tan( {27}^{ \circ} )}}$

$\\ \implies \sf y = { \underbrace{ \sf \: \tan( {9}^{ \circ} ) \cot( {90}^{ \circ} - {81}^{ \circ})}} \tan( {60}^{ \circ} ){ \underbrace{ \sf \tan( {63}^{ \circ}) \cot( {90}^{ \circ} - {27}^{ \circ} )}}$

$\\ \implies \sf y = { \underbrace{ \sf \: \tan( {9}^{ \circ} ) \cot( {9}^{ \circ})}} \tan( {60}^{ \circ} ){ \underbrace{ \sf \tan( {63}^{ \circ}) \cot( {63}^{ \circ}}}$

• We also know that –

$\\ \dashrightarrow \sf \: \tan( \theta) = \dfrac{1}{ \cot( \theta)}$

$\\ \implies \sf y = \: \tan( {9}^{ \circ} ) \times \dfrac{1}{ \tan( {9}^{ \circ})} \times \tan( {60}^{ \circ} ) \times \tan( {63}^{ \circ}) \times \dfrac{1}{ \tan( {63}^{ \circ}}$

$\\ \implies \sf y = \tan( {60}^{ \circ} )$

$\\ \implies \large{ \boxed{ \sf y = \sqrt{3} }}$

• Hence , Option (3) is correct.