2026 · Q95
For the next two (02) items that follow:
p·sin²α + q·cos²α = m and p·cos²β + q·sin²β = n.
95. What is tan²α equal to?
Elementary MathematicsTrigonometry
- A(m−q)/(p−m)
- B(m−p)/(q−m)
- C(m−q)/(m−p)
- D(m−p)/(m−q)
Explanation
Put t=tan²α, so sin²α=t/(1+t), cos²α=1/(1+t): pt+q=m(1+t), giving t(p−m)=m−q, i.e. tan²α=(m−q)/(p−m), option A. Writing sin²α and cos²α in terms of tan²α is the standard substitution that linearises the equation.