Practice30Create account

If 5(secθ − tanθ) = 3, then 5(secθ + tanθ) equals:

Competition practiceTrigonometry
  • A5/3
  • B1/3
  • C25/3
  • D3

Step-by-Step Solution

The given statement says secθ − tanθ = 3/5, and because (secθ + tanθ)(secθ − tanθ) = seθ − taθ = 1, the companion is secθ + tanθ = 5/3. The question asks for FIVE times that, namely 25/3 ≈ 8.33. Check: secθ − tanθ = 0.6 and secθ + tanθ = 1.667 give secθ = 1.1333 and tanθ = 0.5333, whose squares differ by exactly 1. Dropping the factor 5 leaves 5/3, taking the reciprocal of the printed number 3 gives 1/3, and simply copying that number gives 3.
Answer: C) 25/3

Master this topic in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Trigonometry practice questions

More Trigonometry practice

A vertical flag mast stands on the top of a hill 50 m high. From a point on the plain in…If p = a·secθ + b·tanθ and q = a·tanθ + b·secθ, then p² − q² equals:How many angles θ with 0° ≤ θ < 360° satisfy cos 2θ = cos θ?Two friends, each with eyes 1.5 m above the ground, stand on level ground on the same…For every acute angle θ, the value of cot²θ − cos²θ − cot²θ·cos²θ is: