Question

if sin^2 theta + sin theta = 1 then find the value of tan^4 - tan^2 theta

plz give correct answer... ​

Answer 1

Step-by-step explanation:

We have,

$\tt{sin^{2} ( \theta) + sin (\theta) = 1}$

$\sf{ \implies \: \dfrac{1}{cosec^{2} ( \theta) }+ \dfrac{1}{cosec(\theta) }= 1}$

$\sf{ \implies \: 1+ cosec(\theta) = cosec^{2} ( \theta)}$

$\sf{ \implies \: cosec(\theta) = cosec^{2} ( \theta) - 1}$

$\sf{ \implies \: cosec(\theta) = cot^{2} ( \theta) }$

$\sf{ \implies \: sin(\theta) = tan^{2} ( \theta) }$

So,

$\sf{ \implies \: sin ^{2} (\theta) = tan^{4} ( \theta) }$

Now,

$\sf{ \implies tan^{4} ( \theta) + tan^{2} ( \theta) = sin ^{2} (\theta) + sin(\theta) = 1}$