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Find the biggest among sin1+cos1, √sin1+√cos1 and √1+sin2

Mayur Reddy , 9 Years ago
Grade 11
anser 1 Answers
jagdish singh singh
\hspace{-0.6 cm}$Here $\sqrt{1+\sin 2} = \sqrt{\sin^21+\cos^2 1+2\sin 1\cdot \cos 1}=\left|\sin 1+\cos 1\right|$\\\\So we get $\sqrt{1+\sin 2}$ = \sin 1+\cos 1.$\\\\$Now Using $\sqrt{\sin 1}>\sin 1$ and $\cos 1>\cos 1\;,$\\\\ Bcz $\sin 1,\cos 1,\sqrt{\sin 1},\sqrt{\cos 1}\in \left(0,1\right)$\\\\So $\sin 1+\cos 1=\sqrt{1+\sin 1}<\sqrt{\sin 1}+\sqrt{\cos 1}$ and Here $1^{c}\approx 57^0$
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