It’s your turn on More inverse trig functions, and a few others

Do your best in trying to solve the following problems. In any case some of them are solved in the video and all of them are solved in the pdf file below.

Exercise 1.

Evaluate the following: [1. arcsin 1;] [2. arcsinleft(sin dfrac{3pi}4right);] [3. cosleft(arcsinleft(dfrac 35right)right);] [4. tanleft(arccosleft(-dfrac 23right)right).]

Exercise 2.

Prove the following identities: [1. sinh(-x)=-sinh x;] [2. cosh(-x)=cosh x;] [3. sinh(x+y)=sinh xcosh y+cosh xsinh y;] [4. cosh(x+y)=cosh xcosh y+sinh xsinh y.]