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 $
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- [JEE MAIN 2023]
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- [IIT 1993]
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Which of the following functions have the maximum value unity ?
Which of the following functions have the maximum value unity ?