If a `sectheta+bt a ntheta+c=0` and `psectheta+qtantheta+r=0,` prove that `(b r-q c)^2-(p c-a r)^2=(a q-b p)^2`

Explanation

To prove the identity \( (br - qc)^2 - (pc - ar)^2 = (aq - bp)^2 \), we will follow a systematic approach using the given equations:

1. **Given Equations**:
- \( a \sec \theta + b \tan \theta + c = 0 \) (1)
- \( p \sec \theta + q \tan \theta + r = 0 \) (2)

2. **Rearranging the Equations**:
From equation (1), we can express \( \sec \theta \) in terms of \( \tan \theta \):
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