What is the first step. Explain please.

Which expression is equivalent to cos^2x + cot^2x + sin2^x?

a) 2csc^2x
b) tan^2x
c) cot^2x
d) csc^2x

cos^2x + cot^2x + sin2^x

1 + cot^2 x

1 + cos^2 x/sin^2 x

sin^2 x/sin^2 x + cos^2 x/sin^2 x

1/sin^2 x

csc^2 x d)

How did you get 1 + cot^2 x?

cos^2 x + sin^2 x = 1

That should be part of your soul !

Thank you~ T.T my school is fast paced, I am trying to keep up...

Ah, the first step in anything is always the hardest. But fear not, my friend! The first step is simply taking a big breath and reminding yourself that you've got this!

Now, onto the expression cos^2x + cot^2x + sin2^x. Let's see which expression is equivalent to it:

a) 2csc^2x - Well, this reminds me of when I was learning the ABCs. "C is for Clown, and Csc is for...wait, what does Csc stand for again?"

b) tan^2x - Ah, the good ol' tangent squared. Who doesn't love a good tan? But does it match our expression?

c) cot^2x - Cot? More like "Cot dayum, I can't remember what Cot stands for either!" Is this the one?

d) csc^2x - Ah, the cosecant squared. Cosecant, could you please cosec-off and let us know if this expression is the right one?

I'm afraid the answer is d) csc^2x. So, the equivalent expression is cos^2x + cot^2x + sin2^x = csc^2x. It looks like the clowns and the sines had a wild party, and the cosecants decided to crash it!

I hope that answers your question and brings a smile to your face!

To determine the first step in simplifying the given expression, we need to break it down and understand the properties of trigonometric functions involved.

The expression is: cos^2x + cot^2x + sin2^x

First, let's identify the terms present in the expression:

Term 1: cos^2x
Term 2: cot^2x
Term 3: sin2^x

To simplify the expression, we need to apply trigonometric identities to the given terms.

Step 1: Use the Pythagorean identity for cos^2x.
The Pythagorean identity states that sin^2x + cos^2x = 1.
Rearranging this equation, we get cos^2x = 1 - sin^2x.

Substituting this result into our expression, we have:
1 - sin^2x + cot^2x + sin2^x

Step 2: Simplify sin2^x using the double-angle identity.
The double-angle identity for sine function is sin2x = 2sinxcosx.

So, the expression becomes:
1 - sin^2x + cot^2x + 2sinxcosx

Now, we have simplified the given expression using trigonometric identities.

To find the equivalent expression, we can compare it with the options provided:

a) 2csc^2x
b) tan^2x
c) cot^2x
d) csc^2x

Examining the simplified expression, we see that it does not match any of the options directly. Therefore, none of the given options is equivalent to the original expression cos^2x + cot^2x + sin2^x.

Thus, the first step in simplifying the given expression is to apply the Pythagorean identity to cos^2x.