Question

Solve the equation: (sec a + tan a) / (1 + sec a - tan a) = [Blank].

Options:
A) sec a - tan a
B) sec a + tan a - 1
C) sec a - tan a - 1
D) sec a + tan a + 1

Answer 1

To solve the given equation, simplify it using trigonometric identities and obtain the answer as 2/tan(a).

Step-by-step explanation:

To solve the equation (sec a + tan a) / (1 + sec a - tan a), we need to simplify it.

We can use the trigonometric identities: tan(a ± ß) = 1/tan(a) ± tan(ß) and sec(a ± ß) = 1/sec(a) ± sec(ß)

So, we rewrite the equation as [(1/tan(a)) + tan(a)] / [1 + (1/sec(a)) - tan(a)]

Simplifying further, we get 2/tan(a).

Therefore, the answer is 2/tan(a).