Recall definitions:
- cosine = adjacent/hypotenuse
- sine = opposite/hypotenuse
- tangent = opposite/adjacent
Use the triangle to define each ratio.
Use Pythagorean theorem:
Question 1
- (sin B)² + (cos B)² =
- (b/c)² + (a/c)² =
- b²/c² + a²/c² =
- (a² + b²)/c² =
- c²/c² =
- 1
Proved
Question 2
- 1/(cos A)² - (tan A)² =
- 1/(b/c)² - (a/b)² =
- c²/b² - a²/b² =
- (c² - a²)/b² =
- b²/b² =
- 1
Proved