Question

Tan9°+Tan81°-Tan27°-Tan63°​

Answer 1

Tan9°+Tan81°-Tan27°-Tan63°=4

Answer is in attachment

Answer 2

Answer:

tan 9° + tan 81° - tan 27° - tan 63°

⇒ tan(9°) + tan(90°-9°) - tan(27°) - tan(90°-27°)

⇒ tan 9° + cot 9° - tan 27° - cot 27°

⇒ tan 9° + cot 9° - ( tan 27° + cot 27° )

⇒ 2/sin 18° - 2/sin 54°

⇒ 2 ( 4 / ( √5 - 1 ) ) - 2 ( 4 / ( √5 + 1 ) )

⇒ 8 / ( √5 - 1 ) - 8 / ( √5 + 1 )

⇒ 8 ( 1 / ( √5 - 1 ) - 1 / ( √5 + 1 )

⇒ 8 ( √5 + 1 - √5 - 1 ) / ( (√5 )² - 1 )

⇒ ( 8 × 2 ) / ( 5 - 1 )

⇒ 16 / 4

⇒ 4

The value will be 4 .

Step-by-step explanation:

Use tan ( 90 - x ) = cot x .

We will use the formula for tan A + cot A

tan A + cot A = 2 / sin 2 A .

Then use sin 18 = ( √5 - 1 ) / 4

Also use sin 54 = ( √5 + 1 ) / 4 .

Use the formulas of ( a + b )( a - b) = a² - b² .