MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 11
        
2sinx+2cosx is  minimum velu
please  get  the  and the sums
one year ago

Answers : (1)

jagdish singh singh
168 Points
							
\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 $x=2n\pi+\frac{5\pi}{4}\;, n\in \mathbb{Z}$
one year ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 31 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details