Prove that: (cosA - sinA +1)/ (cosA +sinA -1) = cotA + cosecA

Answer:





To solve these types of question, in most of the cases, you will need to take the minus sign common in both numerator and denominator for easiness.

Then you need to rationalize the denominator.

After that you will need to open up the two formulas. I.e. (a-b)²  in the numerator and a²-b² in the denominator.

Then you have to use a Trigonometric identity:

Sin²A + cos²A = 1
Then solve the question as shown in the image.

At last after doing basic Mathematical operations, you will need to remember

1/ sinA = cosecA and cosA/sinA = cotA

This is how you prove the given trigonometric identity in Trigonometry of Mathematics.

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