Can someone prove b.,c., and d.? i need !

Proofs are in the explanation.

Step-by-step explanation:

b)  My first thought is to divide top and bottom on the left hand side by .

I see this would give me 1 on top and where that sine is, it would give me tangent since sine/cosine=tangent.

Let's do it and see:

c) My first idea here is to expand the cos(x+y) using the sum identity for cosine.

So let's do that:

Separating the fraction:

The cos(x) cancel's in the first fraction and the sin(y) cancels in the second fraction:

d) This one makes me think it is definitely essential that we use properties of logarithms.

The left hand side can be condense into one logarithm using the product law:

We are multiplying conjugates inside that natural log so we only need to multiply the first and the last:

I can rewrite using the Pythagorean Identity:

:

Now by power rule for logarithms:

true

step-by-step explanation: