Question

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please help in finding the answer do it fast
prove that
sin Ф / cotФ + cosec Ф = 2 +(sin Ф / cot Ф - cosec Ф)
sin theeta divided by cot theeta + cosec theeta = 2 + (sin theta divided by cot theta - cosec theta)

Answer 1

hello here is u r ans

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Answer 2

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

To Prove :

$\frac{\sin\theta}{\cot\theta+\csc\theta}=2+\frac{\sin\theta}{\cot\theta-\csc\theta}$

L.H.S.

$\frac{\sin\theta}{\cot\theta+\csc\theta}\\\\\text{Rationalizing the above expression}\\\\\implies \frac{\sin\theta(\csc\theta-\cot\theta)}{\csc^2\theta-\cot^2\theta}\\\\\implies 1-\cos\theta$

R.H.S.

$2+\frac{\sin\theta}{\cot\theta-\csc\theta}\\\\\text{Rationalizing the above expression}\\\\\implies 2+\frac{\sin\theta(\cot\theta+\csc\theta)}{\cot^2\theta-\csc^2\theta}\\\\\implies 2+\frac{\cos\theta+1}{-1}\\\\\implies 2-\cos\theta-1\\\\\implies 1-\cos\theta$

Therefore, L.H.S. = R.H.S.

Hence Proved.