Question

(3 tan 15°)-(tan^3 15°)÷(1-3tan^2 15°)
=​

Answer 1

EXPLANATION.

⇒ [(3tan15°) - (tan³15°)]/[1 - 3tan²15°].

As we know that,

Formula of :

⇒ tan3θ = (3tanθ - tan³θ)/(1 - 3tan²θ).

Using this formula in this question, we get.

⇒ [(3tan15°) - (tan³15°)]/[1 - 3tan²15°] = tan 3(15°).

⇒ [(3tan15°) - (tan³15°)]/[1 - 3tan²15°] = tan(45°).

⇒ [(3tan15°) - (tan³15°)]/[1 - 3tan²15°] = 1.

∴ The value of [(3tan15°) - (tan³15°)]/[1 - 3tan²15°] is equal to 1.

                                                                                                                 

MORE INFORMATION.

Trigonometric ratios of multiple angles.

sin2θ = 2sinθcosθ = 2tanθ/(1 + tan²θ).

cos2θ = 2cos²θ - 1 = 1 - 2sin²θ = cos²θ - sin²θ = (1 - tan²θ)/(1 + tan²θ).

tan2θ = 2tanθ/(1 - tan²θ).

sin3θ = 3sinθ - 4sin³θ.

cos3θ = 4cos³θ - 3cosθ.

tan3θ = (3tanθ - tan³θ)/(1 - 3tan²θ).