Question

if tana +cota=2then what is the value of tansqareA+cot sqareA​

Answer 1

Given:

• tan A + cot A = 2

To find:

1. tan² A + cot² A = ?

Method:

We know that  tan A + cot A = 2

Squaring on both sides,

(tan A + cot A)² = 2²

Splitting (tan A + cot A)² using the identity, (a + b)² = a² + b² + 2ab

⇒ tan²A + cot²A + 2tanA.cotA = 4

⇒ tan²A + cot²A + 2×tanA×1/tanA = 4

⇒ tan²A + cot²A + 2 = 4

⇒ tan²A + cot²A = 4 - 2

⇒ tan²A + cot²A = 2

Additional Information:

1. Theta(θ) is defined as any one of the 2 acute angles.
2. tanθ is sinθ divided by cotθ
3. cotθ is the reciprocal of tanθ
4. Reciprocal of sinθ is cosecθ
5. Reciprocal of cosθ is secθ