Question

If cot theta is equal to 4 / 3 then find the value of cosecant squared theta + 1

Answer 1

Step-by-step explanation:

cot theta = 4/3

so cosec theta = 5/3

cosec squared theta = 25/9

cosec squared theta + 1 = 25/9 + 1 = 34/9

Answer 2

The value of $\csc^2 \theta+1$ is equal to $\dfrac{34}{9}$.

Step-by-step explanation:

We have,

$\cot \theta=\dfrac{4}{3}$

To find, the value of $\csc^2 \theta+1$ = ?

∴ $\csc^2 \theta+1$

Using the trigonometric identity,

$\csc^2 \theta-\cot^2 \theta$ = 1

⇒ $\csc^2 \theta$ = 1 + $\cot^2 \theta$

∴ $\csc^2 \theta+1$

= 1 + $\cot^2 \theta$ + 1

= 2 + $\cot^2 \theta$

= 2 + $(\dfrac{4}{3})^2$

= 2 + $\dfrac{16}{9}$

= $\dfrac{18+16}{9}$

= $\dfrac{34}{9}$

∴ The value of $\csc^2 \theta+1$ = $\dfrac{34}{9}$

Thus, the value of $\csc^2 \theta+1$ is equal to $\dfrac{34}{9}$.