Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

See explanation.

Step-by-step explanation:

The hyperbolic sine and cosine functions are defined as follows:

We want to show that:

We use the definition by substituting the expressions into the left hand side and simplify to obtain the RHS.

b)

If we start with the identity in a) and we divide both sides by cosh²x we get:

This simplifies to:

1. d.90

2. e. none of these (80)

3. a. 0

4. b. 6

5. e. none of these (10)

6. a. 5

can you rephrase the question ? it is unclear : -)

step-by-step explanation: