Question

If cosec θ = `5/3`, then sin²x + cos²x + 1 is equal to ______.

Options

• 0

• `25/9`

• 2

• `9/25`

Answer 1

If cosec θ = `5/3`, then sin²x + cos²x + 1 is equal to 2.

Explanation:

For any angle θ,

sin²θ + cos²θ = 1   ...(Pythagorean identity)

So, sin²θ + cos²θ + 1

= 1 + 1

= 2

Also, cosec θ = `5/3` implies `sin θ = 1/("cosec"  θ) = 3/5`, which is consistent but unnecessary because sin²θ + cos²θ = 1 holds for all θ.