Question

If secθ+tanθ=k, then secθ-tanθ=?

• A. \(k\)
• B. \(\frac 1k\)
• C. \(k^2\)
• D. \(\frac {1}{k^2}\)

Answer 1

The Correct Option is B

We are given that $\sec \theta + \tan \theta = k$. 
We want to find the value of $\sec \theta - \tan \theta$. 
We know the trigonometric identity: $$ \sec^2 \theta - \tan^2 \theta = 1 $$ 
We can factor the left side as a difference of squares: $$ (\sec \theta + \tan \theta) (\sec \theta - \tan \theta) = 1 $$ We are given that $\sec \theta + \tan \theta = k$. Substituting this into the equation, we get: $$ k (\sec \theta - \tan \theta) = 1 $$ Dividing both sides by $k$, we have: $$ \sec \theta - \tan \theta = \frac{1}{k} $$