How do you prove #(1 + cot²θ) / secθ = cscθcotθ#?
For this particular problem, we can make use of a trigonometric identity, namely
Modifying the left-hand side, we can write
Now, we can use the reciprocal identities of
Replacing the left-hand side with these reciprocal identities we get
To make the left-hand side a lot easier, we can multiply both the numerator and denominator by the reciprocal of the denominator, namely
By converting the left-hand side back to it's original identities, we can conclude that it does, in fact, equal to the right-hand side.
Thus, we have verified this equation.
I recommend modifying one side only, just so it is much clearer as to what is going on in the first place. These problems mostly require trigonometric identities and reciprocal identities, so make sure you know how to use them.