Question

The value of tan 81° – tan63 tan27° + tan9° is
(a) 1 (b) 2 (c) 3 (d) 4 (e) 6​

Answer 1

the ans is E which most aprox to 5.64

Answer 2

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$\mathtt{\huge{\underline{\red{Answer\: :}}}}$

$\: \large \red{ \bold{ \underline{step \: by \: step \: explaination }}}$

$\bf \: tan81 \degree - tan63 \degree - tan27 \degree + tan9 \degree$

$\: \\ \implies \sf \: tan 81 \degree - tan63 \degree - tan27 \degree + tan9 \degree$

$\: \\ \implies \sf \: tan81 \degree \: + tan9 \degree - (tan63 \degree + tan27 \degree$

$\\ \implies \sf \: cot \: 9 \degree + tan9 \degree - (cot27 \degree + tan27 \degree)$

$\: \\ \implies \displaystyle \sf \: \frac{ {(cos9 \degree})^{2} + ( {sin9 \degree)}^{2} }{sin9.cos9} - \frac{( {cos27 \degree)^2 + (sin27 \degree)}^{2} }{sin27 \degree.cos27 \degree}$

$\: \\ \implies \displaystyle \sf \: \frac{1}{sin9 \degree.cos9 \degree} - \frac{1}{sin27 \degree .cos27 \degree}$

$\: \implies \displaystyle \sf \: \frac{2}{sin18 \degree} - \frac{2}{sin54 \degree}$

$\: \implies \displaystyle \sf \: 2 \times \frac{sin54 \degree - sin18 \degree}{sin54 \degree.sin18 \degree}$

$\: \implies \displaystyle \sf \: \frac{4cos36 \degree \: sin18 \degree}{cos36 \degree \: sin18 \degree}$

$\: \implies \displaystyle \sf \: \frac{4 \cancel{cos36 \degree \: sin18 \degree}}{ \cancel{cos36 \degree \: sin18 \degree}}$

$\: \implies \bf{ \underline{the \: answer \: will \: be \: 4}}$

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❄ Hope this answer helps u ⛄ ⛄