Question

(cosec A - sin A)(sec A - cos A) =
tan A + cot A​

Answer 1

Answer:

1

How can I prove that (cosec A-sin A) (sec A- cos A) =1/tan A+ cot A?

Somnath Dwivedi

Answered May 15, 2018

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.

Answer 2

Step-by-step explanation:

A ka matlab thita na aapne likha