Question

Use the pythagorean identity to prove that cot²Ф + 1 = csc²Ф for all values of Ф where sine does not equal 0

Answer 1

Answer: TRUE

Explanation:

For the sake of typing this easier, I'm going to omit using theta however the final answer will have it.

RH:

Knowing that csc = 1/sin, csc² = 1/sin²

LH:

Knowing that cot = cos/sin, cot² = cos²/sin²

Another important trig identity is sin² + cos ² = 1

So therefore you now have:

cos²/sin² + sin² + cos²

Put everything under the same denominator:

cos² + sin²*sin² + cos²*sin² / sin²

= cos² + sin²(sin² + cos²) / sin²

= cos² + sin² (1) / sin²

= 1 * 1 / sin²

= 1 / sin²

Therefore this trig identity is true