Question

If the value of sin A = 3/4, then find the value of 3(cosec² A + 2cot² A) - 4?
1. 4
2. 6
3. 3
4. 2

Answer 1

Correct Answer - Option 2 : 6

Given:

sin A = 3/4

Identity used:

In a right angled triangle;

sin θ = Perpendicular/Hypotenuse

cot θ = Base/Perpendicular

cosec θ = 1/sin θ 

Pythagorus theorem;

(Hypotenuse)² = (Base)² + (Perpendicular)² 

Calculation:

∵ sin A = P/H

sin A = 3/4

∴ In right angled triangle;

Perpendicular = 3

Hypotenuse = 4

Base = √(4² - 3²)

= √(16 - 9)

= √7

∴ cot A = (√7)/3

∴ 3(cosec2 A + 2cot2 A) - 4 = 3 × [(4/3)² + 2((√7)/3)²] - 4

= 3 × [(16/9) + 2(7/9)] - 4

= 3 × [(16/9) + (14/9)] - 4

= 3 × (30/9) - 4

= 10 - 4

= 6