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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!

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!