Question

9. If tan A + cot A =2 the find the value of tan2A+cot2A​

Answer 1

Step-by-step explanation:

Given:-

Tan θ + Cot θ = 2

To find:-

Find the value of Tan^2 θ + Cot^2 θ ?

Solution:-

Given that :-

Tan θ + Cot θ = 2

On squaring both sides then

=> (Tan θ + Cot θ)^2 = 2^2

=>(Tan θ + Cot θ)^2 = 4

LHS is in the form of (a+b)^2

Where a = Tan θ and b = Cot θ

We know that

(a+b)^2 = a^2 +2ab +b^2

=> Tan^2 θ + 2 Tan θ Cot θ + Cot^2 θ = 4

We know that

Cot θ = 1/Tan θ

=> Tan^2 θ +2Tan θ (1/Tan θ) + Cot^2 θ = 4

=> Tan^2 θ +( 2 Tan θ/Tan θ) + Cot^2 θ = 4

=> Tan^2 θ + 2 + Cot^2 θ = 4

=> Tan^2 θ + Cot^2 θ = 4 - 2

=> Tan^2 θ + Cot^2 θ = 2

Answer:-

The value of Tan^2 θ + Cot^2 θ for the given problem is 2

Used formulae:-

• (a+b)^2 = a^2 +2ab +b^2

• Cot θ = 1/Tan θ