For any $\theta \, \in \,\left( {\frac{\pi }{4},\frac{\pi }{2}} \right)$, the expression $3\,{\left( {\sin \,\theta - \cos \,\theta } \right)^4} + 6{\left( {\sin \,\theta + \cos \,\theta } \right)^2} + 4\,{\sin ^6}\,\theta $ equals
For any $\theta \, \in \,\left( {\frac{\pi }{4},\frac{\pi }{2}} \right)$, the expression $3\,{\left( {\sin \,\theta - \cos \,\theta } \right)^4} + 6{\left( {\sin \,\theta + \cos \,\theta } \right)^2} + 4\,{\sin ^6}\,\theta $ equals
- [JEE MAIN 2019]
- A
$13 - 4\,{\cos ^2}\,\theta \, + 6\,{\sin ^2}\,\theta \,{\cos ^2}\,\theta $
- B
$13 - 4\,{\cos ^6}\,\theta \,$
- C
$13 - 4\,{\cos ^2}\,\theta \, + 6\,\,{\cos ^4}\,\theta $
- D
$13 - 4\,{\cos ^4}\,\theta \, + 2\,{\sin ^2}\,\theta \,{\cos ^2}\,\theta $
Similar Questions
$\tan 75^\circ - \cot 75^\circ = $
$\tan 75^\circ - \cot 75^\circ = $
If $\cos \left( {\alpha + \beta } \right) = \frac{4}{5}$ and $\sin \left( {\alpha - \beta } \right) = \frac{5}{{13}}$,where $0 \le \alpha ,\beta \le \frac{\pi }{4}$ . Then $\tan 2\alpha =$
If $\cos \left( {\alpha + \beta } \right) = \frac{4}{5}$ and $\sin \left( {\alpha - \beta } \right) = \frac{5}{{13}}$,where $0 \le \alpha ,\beta \le \frac{\pi }{4}$ . Then $\tan 2\alpha =$
- [IIT 1979]
If $A + B + C = \frac{\pi }{2}$ ,then value of $tanA\,\, tanB + tanB\,\, tanC + tanC\,\, tanA$ is
If $A + B + C = \frac{\pi }{2}$ ,then value of $tanA\,\, tanB + tanB\,\, tanC + tanC\,\, tanA$ is
Prove that $\cot x \cot 2 x-\cot 2 x \cot 3 x-\cot 3 x \cot x=1$
Prove that $\cot x \cot 2 x-\cot 2 x \cot 3 x-\cot 3 x \cot x=1$
The sum of all values of $\theta \, \in \,\left( {0,\frac{\pi }{2}} \right)$ satisfying ${\sin ^2}\,2\theta + {\cos ^4}\,2\theta = \frac{3}{4}$ is
The sum of all values of $\theta \, \in \,\left( {0,\frac{\pi }{2}} \right)$ satisfying ${\sin ^2}\,2\theta + {\cos ^4}\,2\theta = \frac{3}{4}$ is
- [JEE MAIN 2019]