Question

if tan A + cot A = 2, then sin 2A =

Answer 1

Given :

• tan A + cot A = 2

To find :

• sin 2A

Concept used :

• tan x = sinx/cos x

• cot x = Cos x / sin x

• Sin 2x = 2 sin x cos x

• sin²x + cos²x = 1

Solution :

$\sf \implies tan \: A + cot \: A = 2$

$\sf \implies \dfrac{sin \: A}{cos \: A} + \dfrac{cos \: A}{sin \: A} = 2$

LCM of cos A and Sin A = Cos A Sin A

$\sf \implies \dfrac{ {sin \:}^{2} A + {cos}^{2} \: A}{cos \: A \: sin \: A} = 2$

$\sf \implies \dfrac{ 1}{cos \: A \: sin \: A} = 2$

$\sf \implies1 = 2 {cos \: A \: sin \: A}$

$\sf \implies1 ={\: sin \: 2 A}$

Answer : 1

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Learn more:-

1. Cosθ = base / hypotenuse

2. cossecθ = 1/ sinθ

3. sec θ = 1/cosθ

4. Cotθ = 1/ tanθ

5. Sin²θ+ Cos²θ= 1

6. Sec²θ - tan²θ = 1

7. cosec ²θ - cot²θ = 1

8. sin(90°−θ) = cos θ

9. cos(90°−θ) = sin θ

10. tan(90°−θ) = cot θ

11. cot(90°−θ) = tan θ

12. sec(90°−θ) = cosec θ

13. cosec(90°−θ) = sec θ

14. Sin2θ = 2 sinθ cosθ

15. cos2θ = Cos²θ- Sin²θ