Let p = tan2α - tanα and q = cotα - cot2α. What is tan²α equal to?
A.(pq)/(p+q)
B.(p+2q)/p
C.p/(p+2q)✓ Correct
D.p/(2p+q)
Explanation
From p/q = tanα·tan2α and using tan2α = 2tanα/(1-tan²α), let t = tan²α. Then p/q = tanα · 2tanα/(1-t) = 2t/(1-t). So p(1-t) = 2qt, giving p = pt + 2qt = t(p+2q), so t = tan²α = p/(p+2q).
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