If \(5\cos\theta=3\), then the value of \(\tan\theta-\sec\theta\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(-\frac{1}{3}\)
From \(\cos\theta\), a right triangle with adjacent side 3 and hypotenuse 5 gives the opposite side by Pythagoras, and then every other ratio.
\(\cos\theta=\frac{3}{5}\), so adjacent \(=3\), hypotenuse \(=5\)
Opposite side \(=\sqrt{5^2-3^2}=\sqrt{16}=4\)
\(\tan\theta=\frac{4}{3}\) and \(\sec\theta=\frac{5}{3}\)
\(\tan\theta-\sec\theta=\frac{4}{3}-\frac{5}{3}=-\frac{1}{3}\)