cos theta . Cosec theta = cot theta...

`cos theta . Cosec theta = cot theta`

Text Solution

Verified by Experts

The correct Answer is:

`cot theta= R.H.S`

NA

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Prove that: sin theta (1 + tan theta) + cos theta (1+ cot theta) = sec theta + cosec theta .

Evaluate the following determinants: (b) |(cos theta, -sin theta),(sin theta, cos theta)| = cos theta (cos theta) - sin theta(-sin theta) = cos^(2) theta + sin^(2) theta = 1

Knowledge Check

( 1 + tan theta + sec theta ) ( 1 + cot theta - cosec theta ) =

A

` 0 `

B

` 1 `

C

` 2 `

D

` - 1 `

(sin theta + cos theta)/(sin theta - cos theta) + (sin theta - cos theta)/(sin theta + cos theta)= ________

A

`(2)/(1-2 cos^(2) theta)`

B

`(2)/(2 sin^(2) theta-1)`

C

Both A and B

D

None of these

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Show that (1)/( cos theta ) -cos theta =tan theta .sin theta

Show that, cot theta.costheta +sin theta = cosec theta

Prove that (cot theta -cos theta )/( cot theta +cos theta ) =(cos ec theta -1)/( cosec theta +1)

Prove that (1+ cot theta + tan theta ) ( sin theta - cos theta) = (sec theta )/(cosec^(2) theta) - (cosec theta)/(sec^(2)theta) .

If cosec theta + cot theta = x , find the value of cosec theta - cot theta .

If cosec theta + cot theta = q , show that cosec theta - cot theta = 1/q and hence find the values of sin theta and sec theta .

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