Krishna
0

Step 1:  Make a note of the given equations

GIVEN: \sec \theta + \tan \theta = p

PROVE:   \sec \theta - \tan \theta = p

Step 1: Search for the appropriate formula among the trigonometric identities

IDENTITY: 1 + \tan^2 \theta = \sec^2 \theta

We can write this as

\sec^2 \theta - \tan^2 \theta = 1

Step 3:  Use the formula of (a + b)(a - b) = a^2 - b^2 to simplify

EXAMPLE:   \sec^2 \theta - \tan^2 \theta = 1

(\sec \theta + \tan \theta)(\sec \theta - \tan \theta) = 1

We know that \sec \theta + \tan \theta = p (given)

p (\sec \theta - \tan \theta) = 1

\sec \theta - \tan \theta = \frac{1}{p}

Therefore, the value of   \sec \theta - \tan \theta = \frac{1}{p}