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JEE Main20236 Apr 2023Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The value of tan 9 o - tan 27 o - tan 63 o + tan 81 o is _____.

Correct answer

0

Step-by-step solution

Given, tan 9 o - tan 27 o - tan 63 o + tan 81 o = cot 81 ° + tan 81 o - tan 27 ° + cot 27 o = tan 9 ° + cot 9 ° - tan 27 ° + cot 27 ° = sin 9 ° cos 9 ° + cos 9 ° sin 9 ° - sin 27 ° cos 27 ° + cos 27 ° sin 27 ° = 2 sin 18 o - 2 sin 54 o = 2 × 4 5 - 1 - 2 × 4 5 + 1 = 8 1 5 - 1 - 1 5 + 1 = 8 5 + 1 - 5 - 1 5 - 1 5 + 1 = 8 2 5 - 1 = 4

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