Addition Formulae of Hyperbolic Functions

If $\tan hx=\frac{1}{2}$ then $\sin h2x-\sec h2x=$

Prove that $2\sin hx\sin hy=\cos h\left(x+y\right)-\cos h\left(x-y\right)$

Prove that $2\cos hx\cos hy=\cos h\left(x+y\right)+\cos h\left(x-y\right)$

Prove that $2\cos hx\sin hy=\sin h\left(x+y\right)-\sin h\left(x-y\right)$

Prove that $\cos hx+\cos hy=2\cos h\left(\frac{x+y}{2}\right)\cos h\left(\frac{x-y}{2}\right)$

Which of the following identitiy is not true?

If $\sinh \left(A\right)=\frac{1}{3}$, find $\sinh \left(3A\right)$. 

If $\tanh \left(A\right)=\frac{5}{12}$, find $\tanh \left(3A\right)$.  [Write the answer in fraction.]

If $\tanh \left(A\right)=\frac{1}{2}$, find $\tanh \left(3A\right)$.  [Write the answer in fraction.]

If $\tanh \left(A\right)=\frac{3}{4}$, find $\tanh \left(3A\right)$.  [Write the answer in fraction.]

Prove that for any $x\in R$, $\tanh \left(3x\right)=\frac{3\tanh \left(x\right)+{\tanh }^3\left(x\right)}{1+3{\tanh }^2\left(x\right)}$.

Prove that $\tanh \left(3A\right)=\frac{7}{9}$ if $\tanh \left(A\right)=\frac{1}{3}$.

If $\cosh \left(A\right)=\frac{1}{3}$, find $\cosh \left(3A\right)$.  [Write the answer in fraction.]

If $\cosh \left(A\right)=\frac{3}{4}$, find $\cosh \left(3A\right)$.  [Write the answer in fraction.]

If $\cosh \left(A\right)=\frac{1}{2}$, find $\cosh \left(3A\right)$.

Prove that $\cosh \left(6A\right)=32{\cosh }^6\left(A\right)-48{\cosh }^4\left(A\right)+18{\cosh }^2\left(A\right)-1$.

Prove that $\cosh \left(3A\right)=4{\cosh }^3\left(A\right)-3\cosh \left(A\right)$.

If $\sinh \left(A\right)=\frac{1}{4},$ find $\sinh \left(3A\right)$.   (Write the answer in fraction.)

If $\sinh \left(A\right)=\frac{3}{4},$ find $\sinh \left(3A\right)$.  (Write the answer in fraction.)

If $\sinh \left(A\right)=\frac{1}{2},$ find $\sinh \left(3A\right)$.