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If the value of sec B + tan B = r, then...

If the value of `sec B + tan B = r`, then the value of sec B - tan B is equal to :

A

0

B

`-r`

C

`(1)/(r)`

D

`r^(2)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we start with the given equation: 1. **Given**: \( \sec B + \tan B = r \) 2. **We need to find**: \( \sec B - \tan B \) 3. **Using the identity**: We know the trigonometric identity: \[ \sec^2 B - \tan^2 B = 1 \] 4. **Factoring the identity**: The left side can be factored as: \[ (\sec B + \tan B)(\sec B - \tan B) = 1 \] 5. **Substituting the known value**: We substitute \( \sec B + \tan B = r \) into the equation: \[ r(\sec B - \tan B) = 1 \] 6. **Solving for \( \sec B - \tan B \)**: To isolate \( \sec B - \tan B \), we divide both sides by \( r \): \[ \sec B - \tan B = \frac{1}{r} \] Thus, the value of \( \sec B - \tan B \) is \( \frac{1}{r} \). ### Final Answer: \[ \sec B - \tan B = \frac{1}{r} \]
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