Question

cot theta - tan theta = 5 , then find cot square theta + tan square theta​

Answer 1

Answer:  27

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given :-

Cot θ - Tan θ = 5

To find :-

Find the value of Cot² θ + Tan² θ ?

Solution :-

Given equation is Cot θ - Tan θ = 5

On squaring both sides then

=> (Cot θ - Tan θ)² = 5²

This is in the form of (a-b)²

Where, a = Cot θ and b = Tan θ

We know that

(a-b)² = a²-2ab+b²

=> Cot² θ - 2 Cot θ Tan θ + Tan² θ = 25

=> Cot² θ - 2(1/Tan θ)( Tan θ) + Tan² θ = 25

=> Cot² θ - 2 (Tan θ /Tan θ) + Tan² θ = 25

=> Cot² θ - 2 (1) + Tan² θ = 25

=> Cot² θ - 2 + Tan² θ = 25

=> Cot² θ + Tan² θ = 25 + 2

=> Cot² θ + Tan² θ = 27

Answer:-

The value of Cot² θ + Tan² θ = 27

Used formulae:-

→ (a-b)² = a²-2ab+b²