Question

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

Answer 1

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Answer 2

Answer:

Option A. $cot\theta = -1$

Step-by-step explanation:

$\frac{tan^{3}\theta -1}{tan\theta -1}-sec^{2}\theta +1=0$

we have to the value of $cot\theta$

We further solve the equation

$\frac{(tan\theta -1)(tan^{2}\theta +1+tan\theta )}{(tan\theta -1)}-sec^{2}\theta+1=0$         [a³- b³= (a-b)(a² + b²+ ab)]

$sec^{2}\theta +tan\theta -sec^{2}\theta +1=tan\theta +1=0$

$\frac{1}{cot\theta }=-1$

$cot\theta = -1$

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