Question

If cosec theta = 3/2, then find the value of 2 ( cosec2 theta + cot2 theta )

Answer 1

7

Explanation:

Using the trigonometric identity

• 1 + cot²x = cosec²x, then

2(cosec²Θ + cosec²Θ - 1 )

= 2(2cosec²Θ - 1)

= 4cosec²Θ - 2

= 4 × (
`(3)/(2)` )² - 2

= 4 ×
`(9)/(4)` - 2

= 9 - 2

= 7