展开 ((tan(a)+cot(a))sin(a))/(csc(a))

解答

展开

\frac{( tan ( a ) + cot ( a ) ) sin ( a )}{csc ( a )}

sec (a) sin (a)

求解步骤

\frac{( tan ( a ) + cot ( a ) ) sin ( a )}{csc ( a )}

乘开

(tan (a) + cot (a)) sin (a) : sin (a) tan (a) + sin (a) cot (a)

= \frac{sin ( a ) tan ( a ) + sin ( a ) cot ( a )}{csc ( a )}

使用基本三角恒等式:

cot (x) = \frac{cos ( x )}{sin ( x )}

= \frac{cos ( a )}{sin ( a )} sin (a)

化简

\frac{cos ( a )}{sin ( a )} sin (a) : cos (a)

= \frac{sin ( a ) tan ( a ) + cos ( a )}{csc ( a )}

化简

sin (a) tan (a) + cos (a) : sec (a)

= \frac{sec ( a )}{csc ( a )}

使用基本三角恒等式:

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

= sec (a) sin (a)

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