# Trig Identities Solver

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In Trigonometry, trigonometric identities are very important as they help us understand the relationship between the 6 trigonometric functions in a much better way. Identities are equations where the given trigonometric expression in the left-hand side of the equation is the same as the trigonometric expression in the right-hand side of the equation. Therefore in order to prove trigonometric identities, we must show that the left side and the right side of the equation are exactly the same!

Example 1: Prove the trigonometric identity: tan(x) * cosec(x) = sec(x).

In order to prove the above given trigonometric identity, we have to first start by picking any side of the equation.

Here let’s start with the left-hand side of the equation -> tan(x) * cosec(x)

We can also write the above expression as: tan(x) * cosec(x) = [sin(x)/ cos(x)] * 1/sin(x)

Now sin(x) in the numerator and the denominator gets cancelled, which gives -> 1/cos(x).

So, 1/cos(x) is also written as sec(x) = right-hand side of the equation!
Hence proved!

Example 2: Prove the given trigonometric identity: tan(x) + sec(x) = [1 + sin(x)] * sec(x).

In order to prove the above given trigonometric identity, we have to first start by picking any side of the equation.

Here let’s start with the left-hand side of the equation ->tan(x) + sec(x)

We can also write the above expression as: tan(x) + sec(x) = [sin(x/cos(x)] + 1/cos(x).

Herecos(x) present in the denominator can be taken as the common denominator.

This gives: -> [1 + sin(x)]/ cos(x) which is re-written as [1 + sin(x)] * sec(x) =right-hand side of the equation!

Hence proved!