2026 · Q96
For the next two (02) items that follow:
p·sin²α + q·cos²α = m and p·cos²β + q·sin²β = n.
96. What is cot²β equal to?
Elementary MathematicsTrigonometry
- A(n−q)/(p−n)
- B(n−p)/(q−n)
- C(n−p)/(n−q)
- D(n−q)/(n−p)
Explanation
Put u=cot²β, so cos²β=u/(1+u), sin²β=1/(1+u): pu+q=n(1+u), giving u(p−n)=n−q, i.e. cot²β=(n−q)/(p−n), option A. This mirrors the previous item with the roles of sine and cosine exchanged.