Prove that: (tanΘ +secΘ -1) / (tanΘ -secΘ +1) = (1+ sinΘ)/cosΘ = secΘ + tanΘ

Answer:


Here in this question we have to show that left side is equal to middle side is equal to right side.

For this question, we will use the Trigonometric identity for value of 1

Sec² x - tan² x= 1

And above identity is a² -b² which can also be written as (a +b)(a -b)

Remember we will only use the identity for the value 1 in numerator not in the denominator.

So, we will take the terms common in numerator and cancel the equal terms of the numerator and denominator.

Then we will make it equal to the right side.

And then again we will solve the left side's value and make it equal to the middle side.

See the figure to understand more about this.

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