Question

1+10sinxcosx-2sin²x ka maximum value​

Answer 1

$\bold { \huge{ \mathfrak{Hello!}}}$

$\bold{f(x) = 1 + 10 \: sin x \: cosx - 2 {sin}^{2} x}$

$\longrightarrow \: f(x) = 1 + 10 \: sin x \: \sqrt{1 - {sin}^{2}x } - 2 {sin}^{2} x$

$\bold{putting \: maximum \: value \: of \: sin \:equal \: to \: 1}$

$\longrightarrow \: f(x)max \: = 1 + 10 \sqrt{1 - 1} - 2$

$\longrightarrow \boxed{ \mathtt{f(x) max= - 1}}$