Verify the given equation:?

The trick is to use identities, and then simplify whatever cancels out, to show that one side becomes the other.

For example, csc(x) = 1/sin(x), and

cot(x) = cos(x)/sin(x)

There are many routes you can use.

For this example, let's begin inside th bracket.

change cot^2(x) = cos^2(x) / sin^2(x)

(1 + cot^2(x)) becomes

(1 + cos^2(x) / sin^2(x))

Put all this bracket under the common denominator sin^2(x)

( sin^2(x)/sin^2(x) + cos^2(x)/sin^2(x) )

pull out the common denominator sin^2(x0

(it divides the whole bracket)

(sin^2(x) + cos^2(x))/sin^2(x)

The numerator is a famous identity, where sin^2 + cos^2 = 1

We have reduced the bracket to

1/sin^2(x)

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Let's now rewrite the entire equation using this substitution

sin(x) (1/sin^2(x)) = csc(x)

one sine below is cancelled by the sine above, leaving

1/sin(x) = csc(x)

which is the definition of a csc = 1/sin

https://www.wolframalpha.com/input/?i=sin%28x%29%2...