Question

prove each fundamental identity without using any of the other fundamental identities. (hint: use the trigonometric ratios with x, y, and r)​

Answer 1

We have

x² + y² = r² and

cot θ = x / y

csc θ = r / y

Now,

1 + cot² θ

= 1 + (x / y)²

= 1 + x² / y²

= y²/y² + x²/y²

= (y² + x²)/y²

= r²/y²

= (r/y)²

= csc² θ

Done.