Question

Tan 9° - Tan 27° - Tan63° +Tan81° ​

Answer 1

Trigonometric Identities:

Sin (90° - θ) = cos θ

Cos (90° - θ) = sin θ

tan (90° - θ) = cot θ

sin2 θ + cos2 θ = 1

2sinθcosθ = sin2θ

CALCULATION:

Given that, tan 9° - tan 27° - tan 63° + tan 81°

As we know that,

As we know that, sin2 θ + cos2 θ = 1

As we know that, 2sinθcosθ = sin2θ

As we know that, (A + B) (A – B) = A2 – B2

= 16/4 = 4