Question

tan theta × tan (90 - theta) =

Answer 1

Tan(@-90)=Tan[-{90-@}] Here @=theta. So, Tan(@-90)=-Tan[90-@] ——(1).

As, Tan(90-x)=Cotx ,where x is any arbitrary angle. Therefore, Tan(@-90)=-Cot@ [Using(1)].

Firstly, take -ve sign as common and proceed as follows: Tan [-(90-θ)] , ———-1. { tan(90-θ) is equal to cot θ.}.

We know that, Tan(-θ) = -tanθ. So, we can write eqn1 as: -tan(90-θ) which finally gives you -cotθ. tan ( θ - 90 ).

Take -ve sign common We get, tan [-(90° - θ )] = - tan (90° - θ ) = - cot θ

Answer 2

Answer:

Step-by-step explanation:

tan(theta)*tan(90-theta) = sin(theta)/cos(theta)*cot(theta)

tan(theta)*tan(90-theta) =sin(theta)/cos(theta)*cos(theta)/sin(theta)

tan(theta)*tan(90-theta) = 1  

[sin(theta)/cos(theta)*cos(theta)/sin(theta) gets cancelled ]