Question

1-tan 2 15 / 1+tan 2 150

Answer 1

Answer :

We know that,

tan150° = tan(180° - 30°) = - tan30° = - 1/√3

⇒ tan²150° = 1/3

∴ (1 - tan²150°)/(1 + tan²150°)

= (1 - 1/3)/(1 + 1/3)

= {(3 - 1)/3}/{(3 + 1)/3}

= (2/3)/(4/3)

= 2/4

= 1/2

Another method.

∴ (1 - tan²150°)/(1 + tan²150°)

= cos(2 × 150°)

= cos300°

= cos(360° - 300°)

= cos60°

= 1/2

#MarkAsBrainliest