证明 tan(2A)=(2tan(A))/(1-tan^2(A))

解答

证明

tan (2 A) = \frac{2 tan ( A )}{1 - tan ^{2} ( A )}

真

求解步骤

tan (2 A) = \frac{2 tan ( A )}{1 - tan ^{2} ( A )}

调整左侧

tan (2 A)

使用三角恒等式改写

tan (2 A)

改写为

= tan (A + A)

使用角和恒等式:

tan (s + s) = \frac{tan ( s ) + tan ( s )}{1 - tan ( s ) tan ( s )}

= \frac{tan ( A ) + tan ( A )}{1 - tan ( A ) tan ( A )}

= \frac{tan ( A ) + tan ( A )}{1 - tan ( A ) tan ( A )}

化简

\frac{tan ( A ) + tan ( A )}{1 - tan ( A ) tan ( A )} : \frac{2 tan ( A )}{1 - tan ^{2} ( A )}

\frac{tan ( A ) + tan ( A )}{1 - tan ( A ) tan ( A )}

p ro v e sin (x) tan (x) sec (x) = sec^{2} (x) - 1

p ro v e tan^{4} (k) - sec^{4} (k) = 1 - 2 sec^{2} (k)

p ro v e 1 - tan^{4} (x) = 2 sec^{2} (x) - sec^{4} (x)

p ro v e sin (π) = sin (- π)

p ro v e csc (t) cot (t) = \frac{1 + cot ^{2} ( t )}{sec ( t )}