Question

Simplify sin theta csc theta - sin^2 theta

cos^2 theta
sin^2 theta
2 sin^2 theta
1

pls help

Answer 1

The answer is cos²Ф ⇒ first answer

Explanation:

* Lets talk about the trigonometry functions

- sin²Ф + cos²Ф=1 ⇒ subtract cos²Ф from each side

∴ sin²Ф = 1 - cos²Ф

- sin²Ф + cos²Ф=1 ⇒ subtract sin²Ф from each side

∴ cos²Ф = 1 - sin²Ф

- cscФ = 1/sinФ ⇒ cscФ × sinФ = (1/sinФ) × sinФ = 1

* Now lets solve the problem sinФ × cscФ - sin²Ф

∵ sinФ × 1/sinФ = 1

∴ sinФ × cscФ - sin²Ф = 1 - sin²Ф

∵ 1 - sin²Ф = cos²Ф

∴ sinФ × cscФ - sin²Ф = cos²Ф

* The answer is cos²Ф