证明 1/(cos(θ)sin(θ))=(csc(θ))/(cos(θ))

解答

证明

\frac{1}{cos ( θ ) sin ( θ )} = \frac{csc ( θ )}{cos ( θ )}

真

求解步骤

\frac{1}{cos ( θ ) sin ( θ )} = \frac{csc ( θ )}{cos ( θ )}

使用基本三角恒等式:

\frac{1}{sin ( x )} = csc (x)

\Rightarrow 真

p ro v e sin (x) (tan (x)) + cos (x) = sec (x)

p ro v e sec (β) - cos (β) = tan (β) sin (β)

p ro v e \frac{sin ( y ^{2} )}{cos ( y )} = sec (y) - cos (y)

p ro v e sin^{2} (\frac{π}{4} - 2 π) = cos^{2} (\frac{π}{4} - 2 π)

p ro v e sec (θ) = tan (θ) csc (θ)