Question

If$si{n}^4\theta +co{s}^4\theta +2si{n}^2\theta .co{s}^2\theta +co{s}^2\theta =2tan\theta –si{n}^2\theta$, then the value of $ta{n}^{1/3}\theta +co{t}^{1/3}\theta$ is

• A. 2
• B. 1
• C. 0
• D. $2^{1/3}$

Answer 1

The correct option is A 2

$si{n}^4\theta +co{s}^4\theta +2si{n}^2\theta .co{s}^2\theta +co{s}^2\theta =2tan\theta –si{n}^2\theta$

$\Rightarrow (si{n}^2\theta +co{s}^2\theta )+co{s}^2\theta +si{n}^2\theta =2tan\theta$

$\Rightarrow 2=2tan\theta$

$\Rightarrow tan\theta =1$

$\therefore$ The value of $ta{n}^{1/3}\theta =(tan\theta {)}^{1/3}+{\left(\frac{1}{tan\theta }\right)}^{1/3}$

$=1^{1/3}+1^{1/3}$

=2