2020 · Q62
What is √((secx - tanx)/(secx + tanx)) equal to?
Elementary MathematicsTrigonometry
- A1/(sinx + cosx)
- B1/(tanx + cotx)
- C1/(secx + tanx)
- D1/(cosec x + cotx)
Explanation
√((secx − tanx)/(secx + tanx)) = (secx − tanx)/√(sec²x − tan²x) = secx − tanx, since sec²x − tan²x = 1. And 1/(secx + tanx) = secx − tanx, so the value is 1/(secx + tanx). The two forms agree because (secx − tanx)(secx + tanx) = sec²x − tan²x = 1.