SS1 Maths Trigonometry

1. Figure: http://img109.imageshack.us/f/trid.jpg/
In the figure, if tanA = 4/3, find AB.

Let AB = y

tanA = BC/AB
4/3 = BC/y
BC = 4y/3 …… [1]

AB² + BC² = AC² (Pythagorean theorem)
y² + BC² = (√5)² …… [2]

Sub. [2] into [1]:
y² + (4y/3)² = (√5)²
y² + 16y²/9 = 5
9(y² + 16y²/9) = 9(5)
9y² + 16y² = 45
25y² = 45
y² = 45/25
y = (√45)/5
y = 3(√5)/5

(The given answer is incorrect.)


2. Simplify the following:
1/cos²(90 – B) - 1/tan²B

1/cos²(90 – B) - 1/tan²B
= 1/sin²B – cos²B/sin²B
= (1 - cos²B)/sin²B
= (sin²B + cos²B - cos²B)/sin²B
= sin²B/sin²B
= 1