Evaluate (1 + cos θ) / (1 - cos θ).

Cos θ or cosine θ represents an acute angle in a right angled triangle and is described as adjacent / hypotenuse

Solution:

To evaluate: (1 + cos θ) / (1 - cos θ)

We can write cos θ  as 1/ sec θ 

⇒ (1 + 1/ sec θ) / (1 - 1/ sec θ)

⇒ (sec θ + 1) / (sec θ - 1)

By multiplying both numerator and denominator with (sec θ - 1) we get,

⇒ (sec² θ - 1² ) / (sec θ - 1)²  [Since, (a + b) (a - b) = a² - b²]

Using trigonometric identity, sec² θ - 1 = tan² θ 

⇒ tan² θ / (sec θ - 1)²

Thus, the value of (1 + cos θ) / (1 - cos θ) is tan² θ / ( sec θ - 1)²

Evaluate (1 + cos θ) / (1 - cos θ).

Summary:

The value of (1 + cos θ) / (1 - cos θ) is tan² θ / ( sec θ - 1)²