Question

prove that (sin theta + cos theta) into (tan theta + cot theta) = ( sec theta + cosec theta)​

Answer 1

Answer:

Step-by-step explanation:

First all you need to do is write ( tan theta+ cot theta ) as (sin theta/cos theta + cos theta/sin theta )

Then, you need to take the L.C.M of the above bracket as

(sin^2 theta + cos^2 theta / cos theta.sin theta ), which makes (sin^2 theta + cos ^2 theta/cos theta.sin theta ) = (1/cos theta.sin theta)

Multiply the first bracket by the second which gives us (sin theta + cos theta/sin theta.cos theta )

Finally put the values separately as (sin theta/cos theta.sin theta)+(cos theta/cos theta.sin theta )

Cancel the ( sin theta ) fron the first bracket and then ( cos theta ) from the second bracket.

What's remaining is (1/cos theta)+(1/sin theta) which can be resubstituted as

(sec theta + cosec theta)

That's all there is to it

Glad to help you out.

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