Question

If cosec theta =3/2. Find the value of 2(cosec2 theta + cot2 theta

Answer 1

Answer:

cosecθ=3/2

2(cosec²θ+cot²θ)

2(cosec²θ+cosec²θ-1)                                           {cosec²θ=1+cot²θ]

2(2cosec²θ-1)

2(2(3/2)²-1)

2(2(9/4)-1)

2(9/2 -1)

2(7/2)

7

Step-by-step explanation:

Answer 2

The value of the given expression is 7.

Step-by-step explanation:

Given that

$\csc\theta=\frac{3}{2}$

The relation between cosecФ and cotФ is

cosec²Ф = 1 + cot²Ф

cot²Ф = cosec²Ф -1

Substituting this value in the given expression

$2(\csc^2\theta+\cot^2\theta)\\\\=2(\csc^2\theta+\csc^2\theta-1)\\\\=2(2\csc^2\theta-1)$

Substituting the value of cosecФ

$2(2\cdot(\frac{3}{2})^2-1)\\\\=2(2\cdot\frac{9}{4}-1)\\\\=2(\frac{9}{2}-1)\\\\=2\cdot\frac{7}{2}\\\\=7$

#Learn More:

1+cot2 theta = cosec2 theta

https://brainly.in/question/11440708