Question

tan (40° + 0) - cot (40° - 0)' is equal to :​

Answer 1

Answer:

Step-by-step explanation:

Note: The question seems to be incorrect. It should be Cot(50-θ) and not Cot(40-θ).

Case 1: If instead of Cot(40-θ) we use Cot(50-θ)

Tan(40+θ) - Cot(50-θ)

= Tan(40+θ) - Cot ( 90 - (40+θ))

= Tan(40+θ) - Tan(40+θ)

= 0

Case 2: Going by given question

Tan(40+θ) - Cot(40 - θ)

= Tan(40+θ) - Cot (90- (50 + θ))

= Tan(40+θ) - Tan (50 + θ)  ( ∵ Cot (90-θ) = tanθ)

The above is of form TanA - TanB.

We know that Tan(A-B) = TanA - TanB/ 1 + TanATanB

=> TanA - TanB = Tan(A-B)(1+TanATanB)

Tan(40+θ) - Tan (50 + θ) = Tan (40+ θ - 50 - θ) ( 1 + Tan(40+θ)Tan(50+θ))

                                         = Tan(- 10) * ( 1 + Tan(40+θ)Tan(50+θ))

                                          = Tan10° (1 + Tan(40+θ)Tan(50+θ))

I donot think we will be be able to find the value for this.