证明 tanh^2(x)+sech^2(x)=1

解答

证明

tanh^{2} (x) + sech^{2} (x) = 1

真

求解步骤

tanh^{2} (x) + sech^{2} (x) = 1

使用双曲函数恒等式:

sech^{2} (x) = 1 - tanh^{2} (x)

sech^{2} (x) + tanh^{2} (x) = 1

\Rightarrow 真

p ro v e csc^{2} (u) - cos (u) sec (u) = cot^{2} (u)

p ro v e \frac{cos ^{2} ( x )}{sin ( x )} + sin (x) = csc (x)

p ro v e - csc^{2} (x) cos^{2} (x) = 1 - csc^{2} (x)

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

p ro v e sin (3 a) = 3 sin (a) - 4 sin^{3} (a)