Hello goldenrollUse , and then

2. If t^(2) = ln(1 + x) − ln(1 − x), what is x in terms of t?

Raise to the power of both sides:

Solve for .

Write the equation as3. What are all solutions of the equation: sin^(2) x + 2 sin x = 5/4?

This is a quadratic in . Factorise and solve.

I'm not quite sure what the square root sign covers here. I assume you mean:4. If f (x) = √4x^(2) + 8, x ≥ 0, what is f ^(− 1) (x)?

So, to find , let . Then

Now make the subject of this equation, to give

So

Let .5. sin(2 cos^(−1) x) is equivalent to

and

Grandad