If $\sin \theta + \cos \theta = x,$ then ${\sin ^6}\theta + {\cos ^6}\theta = \frac{1}{4}[4 - 3{({x^2} - 1)^2}]$ for
If $\sin \theta + \cos \theta = x,$ then ${\sin ^6}\theta + {\cos ^6}\theta = \frac{1}{4}[4 - 3{({x^2} - 1)^2}]$ for
- A
All real $x$
- B
${x^2} \le 2$
- C
${x^2} \ge 2$
- D
None of these
Similar Questions
If $\alpha ,\,\,\beta ,\gamma ,\,\,\delta $ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$, then the value of $4\,\sin \frac{\alpha }{2} + 3\,\sin \frac{\beta }{2} + 2\,\sin \frac{\gamma }{2} + \sin \frac{\delta }{2}$ is equal to
If $\alpha ,\,\,\beta ,\gamma ,\,\,\delta $ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$, then the value of $4\,\sin \frac{\alpha }{2} + 3\,\sin \frac{\beta }{2} + 2\,\sin \frac{\gamma }{2} + \sin \frac{\delta }{2}$ is equal to
$\tan 20^\circ \tan 40^\circ \tan 60^\circ \tan 80^\circ = $
$\tan 20^\circ \tan 40^\circ \tan 60^\circ \tan 80^\circ = $
- [IIT 1974]
If $A$ lies in the third quadrant and $3\,\tan A - 4 = 0,$ then $5\,\sin 2A + 3\,\sin A + 4\,\cos A = $
If $A$ lies in the third quadrant and $3\,\tan A - 4 = 0,$ then $5\,\sin 2A + 3\,\sin A + 4\,\cos A = $
If $\alpha + \beta = \frac{\pi }{2}$ and $\beta + \gamma = \alpha ,$ then $\tan \,\alpha $ equals
If $\alpha + \beta = \frac{\pi }{2}$ and $\beta + \gamma = \alpha ,$ then $\tan \,\alpha $ equals
- [IIT 2001]
If $\cos 3\theta = \alpha \cos \theta + \beta {\cos ^3}\theta ,$ then $(\alpha ,\beta ) = $
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