Question

determine o valor de A= cotg x - 1/cossec x - sec x, dado cos x = 1/2

Answer 1

$senx=\sqrt{1-cos^2x}\\ \\ senx=\sqrt{1-(\frac{1}{2})^2}\\ \\ senx=\sqrt{1-\frac{1}{4}}\\ \\ senx=\sqrt{\frac{3}{4}}=\frac{\sqrt3}{2}$

$A=cotgx-\frac{1}{cossecx}-secx\\ \\ A=\frac{cosx}{senx}-senx-\frac{1}{cosx}\\ \\ A=\frac{\frac{1}{2}}{\frac{\sqrt3}{2}}-\frac{\sqrt3}{2}-2\\ \\ A=\frac{1}{2}*\frac{\sqrt3}{2}-\frac{\sqrt3}{2}-2\\ \\ A=\frac{\sqrt3}{4}-\frac{\sqrt3}{2}-2=\frac{\sqrt3-2\sqrt3-4}{4}=\frac{-\sqrt3-4}{4}$