2026 · Q98
For the next two (02) items that follow:
p + q·cotθ = 3·cosecθ and q − p·cotθ = 2·cosecθ.
98. What is tanθ equal to?
Elementary MathematicsTrigonometry
- A(2p + 3q)/(3q − 2p)
- B(2q − 3p)/(3q + 2p)
- C(3q + 2p)/(2q − 3p)
- D(3q − 2p)/(2q + 3p)
Explanation
Treat the equations as linear in cotθ and cosecθ: eliminating gives (p²+q²)cotθ=(3q−2p)cosecθ and (p²+q²)=(3p+2q)cosecθ. Hence tanθ=(3p+2q)/(3q−2p)=(2p+3q)/(3q−2p), option A. Eliminating cosecθ between the two derived relations is what isolates tanθ.