Question

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Answer 1

Explanation:

`(cot \theta)/(cosec \theta + 1) = \frac{cosec\theta -1} {cot \theta}`

`L H S`

`(cot \theta )/(cosec \theta + 1 ) * (cosec \theta - 1)/(cosec \theta -1)`
`[ \ multiplying \ and \ dividng \ by \ (cosec \theta - 1) \ ]`

`= (cot \theta * (cosec \theta - 1))/((cosec ^2\theta -1))`
`[ \ (a -b)(a+b) = a^2 - b^2 \ ]`

`= (cot \theta * (cosec \theta - 1))/(cot^2 \theta)\\ \\`
`[ \ cosec^2\theta - 1 = cot^2 \theta \ ]`

`= (cosec \theta - 1 )/(cot \theta) \\\\= RHS`

Answer 2

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