Question

(cosecA - sin A) ( sec A - cos A) = 1\tan A + cot A
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Answer 1

Answer:

We have to just simplify both side of the question.

Now, taking L. H. S =

(cosecA - sinA)×(secA - cosA)

= (1/sinA - sinA)×(1/cosA - cosA)

= (1-sin²A)/sinA × (1-cos²A)/cosA

= cos²A/sinA × sin²A/cosA

= cos²Asin²A/cosAsinA

= cosAsinA

Now, R. H. S =

1/(tanA + cotA)

= 1/(sinA/cosA + cosA/sinA)

= 1/[(sin²A + cos²A)/cosAsinA]

= 1/[(1/cosAsinA)]

= cosAsinA

Since L. H. S. = R. H. S