Rewrite the expression as a single trigonometric ratio.
A)csc θ
B)1/cos θ
C)sin θ
D)sec θ
sinθ / (1 - cos²θ)
Since sin²θ + cos²θ = 1
---> sin²θ = 1 - cos²θ
So: sinθ / (1 - cos²θ) = sinθ / sin²θ = 1 / sinθ = cscθ
Trig is easier if you can remember the Pythagorean Identity in its three forms:
sin²θ + cos²θ = 1 sin²θ = 1 - cos²θ cos²θ = 1 - sin²θ
Also, there are two more that derive from the above:
1 + tan²θ = sec²θ 1 + cot²θ + csc²θ
sinθ / (1 - cos²θ)
Since sin²θ + cos²θ = 1
---> sin²θ = 1 - cos²θ
So: sinθ / (1 - cos²θ) = sinθ / sin²θ = 1 / sinθ = cscθ
Trig is easier if you can remember the Pythagorean Identity in its three forms:
sin²θ + cos²θ = 1 sin²θ = 1 - cos²θ cos²θ = 1 - sin²θ
Also, there are two more that derive from the above:
1 + tan²θ = sec²θ 1 + cot²θ + csc²θ