Question

Given that tan (A+B) = (tanA + taB)/ (1+tanAtanB) Find the value of tan 75°​

Answer 1

Answer:

Let A= 45° B= 30°

then,

tan75°= tan(45°+30°)= (tan45°+tan30°)/(1-tan45°.tan30°)

= [1+(1/√3)]/[1-(1/√3)]

=(√3+1)/(√3-1) Ans.

or,

= (√3+1)²/2

= (4+2√3)/2

=2+√3 Ans.

Answer 2

EXPLANATION.

To find value of tan 75°.

As we know that,

Formula of :

⇒ tan(A + B) = [tan(A) + tan(B)/1 - tan(A).tan(B)].

⇒ tan(75°) = tan(45°) + tan(30°).

⇒ tan(45°) = 1.

⇒ tan(30°) = 1/√3.

Using this formula in the equation, we get.

⇒ tan(75°) = [tan(45°) + tan(30°)/1 - tan(45°).tan(30°)].

⇒ tan(75°) = [1 + 1/√3]/[1 - 1 x 1/√3].

⇒ tan(75°) = (√3 + 1)/(√3 - 1).

                                                                                                                 

MORE INFORMATION.

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

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

(3) tan2θ = 2tanθ/1 - tan²θ.

(4) sin3θ = 3sinθ - 4sin³θ.

(5) cos3θ = 4cos³θ - 3cosθ.

(6) tan3θ = 3tanθ - tan³θ/1 - 3tan²θ.