Question

The value of tan81 - tan63 - tan27 + tan9 is......
(angles are in degrees)

Answer 1

Answer:

4

Step-by-step explanation:

Tan81 - Tan63 - Tan27 + Tan9

Tan(90 -9) + Tan9 - Tan(90 - 27) - Tan27  (∵ Tan (90 - θ) = Cotθ)

= Cot9 + Tan9 - (Cot27 + Tan27)

= Cos9/Sin9 + Sin9/Cos9 - (Cos27/Sin27 + Sin27/Cos27)

= Cos²9 + Sin²9/Sin9Cos9 - (Cos²27 + Sin²27/Cos27Sin27)

= 1/Sin9Cos9 - 1/Sin27Cos27

= 2/2Sin9Cos9 - 2/2Sin27Cos27

= 2/Sin18 - 2/Sin54

= 2. Sin54 - Sin18/Sin54Sin18

= 2. 2Cos36Sin18/Sin54.Sin18 ( ∵ SInA - SinB = 2Cos(A+B/2)Sin(A-B/2)

= 4. Cos36SIn18/SIn(90-36)Sin18

= 4. Cos36SIn18/Cos36Sin18                 (∵Sin (90 - θ) = Cosθ)

= 4.

Answer 2

Answer:

kavin6502

24.10.2019

Math

Secondary School

+10 pts

Answered

The value of tan81 - tan63 - tan27 + tan9 is......

(angles are in degrees)

1

SEE ANSWER

ADD ANSWER

Answers

kavin6502 is waiting for your help.

Add your answer and earn points.

Spiderman2019Maths AryaBhatta

Answer:

4

Step-by-step explanation:

Tan81 - Tan63 - Tan27 + Tan9

Tan(90 -9) + Tan9 - Tan(90 - 27) - Tan27 (∵ Tan (90 - θ) = Cotθ)

= Cot9 + Tan9 - (Cot27 + Tan27)

= Cos9/Sin9 + Sin9/Cos9 - (Cos27/Sin27 + Sin27/Cos27)

= Cos²9 + Sin²9/Sin9Cos9 - (Cos²27 + Sin²27/Cos27Sin27)

= 1/Sin9Cos9 - 1/Sin27Cos27

= 2/2Sin9Cos9 - 2/2Sin27Cos27

= 2/Sin18 - 2/Sin54

= 2. Sin54 - Sin18/Sin54Sin18

= 2. 2Cos36Sin18/Sin54.Sin18 ( ∵ SInA - SinB = 2Cos(A+B/2)Sin(A-B/2)

= 4. Cos36SIn18/SIn(90-36)Sin18

= 4. Cos36SIn18/Cos36Sin18 (∵Sin (90 - θ) = Cosθ)

= 4.