Question

If (tan^3 theta -1) / (tan theta - 1) - sec^2 theta +1 = 0, find cot theta.

a. -1 b.0 c. 1 d. sec theta

Answer 1

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Answer 2

Option A.
`cot\theta = -1`

Explanation:

`(tan^(3)\theta -1)/(tan\theta -1)-sec^(2)\theta +1=0`

we have to the value of
`cot\theta`

We further solve the equation

`((tan\theta -1)(tan^(2)\theta +1+tan\theta ))/((tan\theta -1))-sec^(2)\theta+1=0` [a³- b³= (a-b)(a² + b²+ ab)]

`sec^(2)\theta +tan\theta -sec^(2)\theta +1=tan\theta +1=0`

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

`cot\theta = -1`

Therefore Option A.
`cot\theta = -1` is the answer.