show that 2 sinx+ 2 cosx 2 1 -1/square root 2 2)if tana and tan b are theroots of equation x 2 +px+qthen1) sin (a+b)=-p 2)tan(a+b)=p/q-1 3)cos a+b)1-q

Question

show that 2 sinx+ 2 cosx >2 1 -1/square root 2 2)if tana and tan b are theroots of equation x 2 +px+qthen1) sin (a+b)=-p 2)tan(a+b)=p/q-1 3)cos a+b)1-q

Vikas TU · Answer

U must know the range of sinx and cosx. similarly sinx lessthan equal to 2 and greater than equal to ½.................(1) 1/2 > = 2^cosx > = 2.............(2) remember cosx is decreasing function hence inequality would change. add both the eqns. we get, 0.5 + 2> = 2^cosx + 2^sinx > = 0.5 + 2 .ie. 2^cosx + 2^sinx subtends at value 2+ 0.5 = 3.5 > 2 1 -1/square root 2 H.P.

Madhav Karnani · Answer

Use A.M. >= G.M. for positive real numbers.2^(sin x) and 2^(cos x) are positive real numbers for all x € R.So, {2^(sin x) + 2^(cos x)}/2 >= sqrt [2^(sin x) × 2^(cos x)] ......... (1)sqrt [2^(sin x) × 2^(cos x)] = 2^{1/2 × (sin (x) + cos (x))}Now, 1/2 × (sin (x) + cos (x)) = 1/sqrt (2) * [ 1/sqrt (2)* sin (x) + 1/sqrt (2)*cos (x)] = 1/sqrt (2) *[ cos (pi/4 - x) ]Now, 2^(sin x) + 2^(cos x) >= 2^[{1/sqrt (2) *cos (pi/4 - x) } +1] ............ (2)***(MULTIPLYING 2 TO BOTH SIDES)Now, -1

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

show that 2 sinx+ 2 cosx >2 1 -1/square root 2 2)if tana and tan b are theroots of equation x 2 +px+qthen1) sin (a+b)=-p 2)tan(a+b)=p/q-1 3)cos a+b)1-q

show that 2^sinx+2^cosx>2^{1 -1/square root 2}
2)if tana and tan b are theroots of equation x²+px+qthen1) sin (a+b)=-p 2)tan(a+b)=p/q-1 3)cos a+b)1-q

2 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

IIT JEE Courses

One Year IIT Programme

Two Year IIT Programme

Crash Course

NEET Courses

One Year NEET Programme

Two Year NEET Programme

One to One

School Board

Live Online classes

Class 11 & 12

Class 9 & 10

Class 6, 7 & 8

Test Series

JEE test series

NEET test series

C.B.S.E test series

Complete Self Study Packages

FULL COURSE

For class 12th

For class 11th

show that 2 sinx+ 2 cosx >2 1 -1/square root 2 2)if tana and tan b are theroots of equation x 2 +px+qthen1) sin (a+b)=-p 2)tan(a+b)=p/q-1 3)cos a+b)1-q

show that 2sinx+2cosx >21 -1/square root 22)if tana and tan b are theroots of equation x2+px+qthen1) sin (a+b)=-p 2)tan(a+b)=p/q-1 3)cos a+b)1-q

2 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

show that 2^sinx+2^cosx>2^{1 -1/square root 2}
2)if tana and tan b are theroots of equation x²+px+qthen1) sin (a+b)=-p 2)tan(a+b)=p/q-1 3)cos a+b)1-q