+91-93193 64476
FlagBACK
Flag Trigonometry> 2 sinx +2 cosx is minimum velu please get...
question mark

2sinx+2cosx is minimum velu
please get the and the sums

suraj , 9 Years ago
Grade 11
anser 1 Answers
jagdish singh singh
\hspace{-0.70 cm}$ Using $\bf{A.M\geq G.M}$ Inequality for $2^{\sin x}\;,2^{\cos x}>0$ \\\\ So $2^{\sin x}+2^{\cos x}\geq 2\cdot 2^{\frac{\sin x+\cos x}{2}}\geq 2\cdot 2^{-\frac{1}{\sqrt{2}}}=2^{1-\frac{1}{\sqrt{2}}}$\\\\ bcz $-\sqrt{2} \leq \sin x+\cos x \leq \sqrt{2}$ for all $x\in \mathbb{R}$\\\\ So $2^{-\sqrt{2}}\leq 2^{\sin x+\cos x}\leq 2^{\sqrt{2}}\Rightarrow 2^{1-\frac{1}{\sqrt{2}}}\leq 2^{\frac{\sin x+\cos x}{2}}\leq 2^{1+\frac{1}{\sqrt{2}}}$\\\\ So $2^{\sin x}+2^{\cos x}\geq 2^{1-\frac{1}{\sqrt{2}}}$ at $x=2n\pi+\frac{5\pi}{4}\;, n\in \mathbb{Z}$
Last Activity: 9 Years ago
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Other Related Questions on trigonometry

question mark
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
1 Answer Available

Last Activity: 3 Years ago

question mark
  • Find the general solution of equation tan3โˆ‚=cot2โˆ‚
For all angles between -720 and +720
trigonometry
1 Answer Available

Last Activity: 3 Years ago

question mark
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
1 Answer Available

Last Activity: 3 Years ago

question mark
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
1 Answer Available

Last Activity: 3 Years ago

question mark
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim๐‘ฅโ†’0 ๐‘ ๐‘–๐‘›6๐‘ฅ/5๐‘ฅ 
trigonometry
1 Answer Available

Last Activity: 4 Years ago