Express tan⁻¹(cos x/(1 − sin x)), Where x ∈ (−3π/2, π/2), in Its Simplest Form
Simplify tan⁻¹(cosx/(1−sinx)) for x∈(−3π/2,π/2) using half-angle substitutions to reveal it equals tan(π/4+x/2), matching the principal range exactly.
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If sec²(tan⁻¹α) + cosec²(cot⁻¹β) = 36 and α + β = 8 With α < β, Then α² + β Is
Given sec²(tan⁻¹α)+cosec²(cot⁻¹β)=36 and α+β=8 with α<β, find α²+β by converting to a system of equations in α+β and αβ.