Question

1) (1 - SinA) (1 + sinA) = COS A
$\cos(?)$
​

Answer 1

cosA x cosA = (1 + sinA)(1 - sinA)

Therefore cos²A = 1 - sin²A

Therefore cos²A + sin²A = 1 , which is one of the definitions, foundations of trigonometry. QED

You want to prove that too? Draw a right-angled triangle with an acute angle A. Label the sides a, b (upright) and h (the hypotenuse).

Well, the definition of cosA is a/h , that of sinA is b/h.

By Pythagoras, a² + b² = h². Therefore (a/h)² + (b/h)² = 1

So we have just proved that sin²A + cos²A = 1 QE..