Trigonometry

Mathematics (NDA)

Title

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The value of tan 9°− tan 27° −tan 63° + tan 81° is equal to-

-1

tan9⁰ – tan27⁰ – tan63⁰ + tan81⁰

Or (tan9⁰ + tan81⁰ ) – (tan27⁰+ tan63⁰ )

Or (tan9⁰ + cot9⁰ )– (tan27⁰ + cot27⁰ )

Or sin9²+ cos9² / sin9⁰cos9⁰ - [ sin27²+cos27² / cos27⁰ sin27⁰ ]

Or 2 / 2 sin9⁰cos9⁰ – 2 / 2 sin27⁰cos27⁰

Or 2 / sin18⁰ – 2 / sin54⁰

Or 2×2cos36⁰ sin18⁰ / sin18⁰ sin54⁰ = 2×2cos36⁰ / cos36⁰ = 4