If m= sin6x + cos6x, then m belongs to the interval


(a) [7/8, 5/4]  (b) [1/2 , 5/8]  (c) [1/4,  1]


Explain pls...

2 years ago

Share

Answers : (1)

                                        

m=sin6x+cos6x=(sin2x+cos2x)(sin4x+cos4x-sin2xcos2x)


as a3+b3=(a+b)(a2-ab+b2)


we know that,


sin2x+cos2x=1


m=((sin2x+cos2x)2-3sin2xcos2x)


m=1-3sin2xcos2x


m=1-3/4(sin2x)2


we know 0<=sin2A<=1,


so -1<=-sin22x<=0 multiply with -1,


-3/4<=-3/4(sin22x)<=0 multiply with 3/4,


1/4<=1-3/4(sin22x)<=1 add 1,


1/4<=m<=1


therefore "m" belongs to[1,1/4].

2 years ago

Post Your Answer

More Questions On Trigonometry

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
Find the exact value of cos(13pi/12)
 
 
Ans: Hello Student, Please find answer to your question below
  img
Jitender Singh 2 months ago
 
Exact answer of cos (13pi/12) is -1.833...... because cos (pi) is always -1
 
Ranganna palem Srikanth 2 months ago
In a triangle ABC the value of acosA+bcosB+cCosC/a+b+c is equal to (A) r/R (b)R/2r (C)R/r (D)2r/R
 
 
Hi, Follow the steps to reach the answer : Apply the cos formula in terms of S, a, b, c. Now rearrange the three terms and apply the formula which will connect R & r to S, a, b, c. You...
  img
Yash Baheti 19 days ago
Whats the cosine rule.
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 2 months ago
limit x-infinity 2^n+1 + 3^n+1 /2^n + 3^n
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 2 months ago
x 1/2 +y=11,x+y 1/2=7
 
 
Hello student, Please find the answer to your question below From(1): x^(1/2) = 7 - y , Letx (1/2) +y=11...........(1) x+y (1/2) =7..........(2) Squaring both sides: x = (7-y)^2 = y^2 - 14y...
  img
SHAIK AASIF AHAMED 14 days ago
View all Questions »