The value of tan 9-tan 27-tan 45-tan 63-tan 81- is

Tan9^∘·tan27^∘·tan45^∘·tan63^∘·tan81^∘ =tan9^∘·tan27^∘·tan45^∘·tan(90 27)^∘·tan(90 9)^∘ =tan9^∘·tan27^∘·tan45^∘·27^∘·9^∘ =(tan9^∘·9^∘)·(tan27^∘·27^∘)·tan45^∘ ...

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Standard XII

Mathematics

Sign of Trigonometric Ratios in Different Quadrants

The value of ...

Question

The value of $tan 9^{\circ} \cdot tan 27^{\circ} \cdot tan 45^{\circ} \cdot tan 63^{\circ} \cdot tan 81^{\circ}$ is

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Solution

$tan 9^{\circ} \cdot tan 27^{\circ} \cdot tan 45^{\circ} \cdot tan 63^{\circ} \cdot tan 81^{\circ} = tan 9^{\circ} \cdot tan 27^{\circ} \cdot tan 45^{\circ} \cdot tan (90 - 27)^{\circ} \cdot tan (90 - 9)^{\circ} = tan 9^{\circ} \cdot tan 27^{\circ} \cdot tan 45^{\circ} \cdot cot 27^{\circ} \cdot cot 9^{\circ} = (tan 9^{\circ} \cdot cot 9^{\circ}) \cdot (tan 27^{\circ} \cdot cot 27^{\circ}) \cdot tan 45^{\circ} = 1 \cdot 1 \cdot 1 = 1$

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Q. The value of

tan 9^{\circ} \cdot tan 27^{\circ} \cdot tan 45^{\circ} \cdot tan 63^{\circ} \cdot tan 81^{\circ}

Q. Find the value of

tan 9^{\circ} - tan 27^{\circ} - tan 63^{\circ} + tan 81^{\circ} .

t a n 9 - t a n 27 - t a n 63 + t a n 81 =

tan $9^{\circ}$ - tan $27^{\circ}$ - tan $63^{\circ}$ + tan $81^{\circ}$ =

tan 9^{\circ} \times tan 27^{\circ} \times tan 63^{\circ} \times tan 81^{\circ}

is equal to

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Sign of Trigonometric Ratios in Different Quadrants

Standard XII Mathematics

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The value of tan9∘⋅tan27∘⋅tan45∘⋅tan63∘⋅tan81∘ is

tan9∘⋅tan27∘⋅tan45∘⋅tan63∘⋅tan81∘=tan9∘⋅tan27∘⋅tan45∘⋅tan(90−27)∘⋅tan(90−9)∘=tan9∘⋅tan27∘⋅tan45∘⋅cot27∘⋅cot9∘=(tan9∘⋅cot9∘)⋅(tan27∘⋅cot27∘)⋅tan45∘=1⋅1⋅1=1

The value of $tan 9^{\circ} \cdot tan 27^{\circ} \cdot tan 45^{\circ} \cdot tan 63^{\circ} \cdot tan 81^{\circ}$ is