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
If sinx+siny=root3(cosy-cosx) Prove that sin3x+sin3y=0.
 
 
Hello students, please check the solution of your question given below: sinx+siny = root3 ( cosx-cosy) 2sin(x+y/2)cos(x-y/2) = root3 {2sin(x+y/2)sin(y-x/2)} sin(x+y/2)[cos(x-y/2)-root3....
  img
Sunil Raikwar 2 months ago
 
Dear student, According to the given relation, we would have: If we multiply both sides by a factor of 4, we get: This on simplifying gives us: If the right hand side can be simplified to...
  img
Sumit Majumdar 2 months ago
solve those questions.
 
 
Hii For a) and f) Use Sin A + Sin B = 2 sin((A+B)/2)cos((A-B)/2) For b) and c) Use CosA + Cos B = 2 cos((A+B)/2)cos((A-B)/2) for d) Use Sin A - Sin B = 2sin((A-B)/2)cos((A+B)/2) for e) Use...
  img
Sourabh Singh one month ago
sinA/2. sin7A/2 + sin 3A/2. sin11A/2 =
 
 
use 2sinAsinB = cos(A_B)-cos(A+B)
 
Sujay 2 months ago
∫cos(2 cot-1​​{ root(1-x/1+x)} = ????
 
 
Ans: Hello Student, Please find answer to your question below
  img
Jitender Singh one month ago
how to find angle made by vector with x-axis
 
 
Say the vector is A. Take dot product with i cap. A.i = |A| . 1 . cos B You know how to calculate A.i. Hence, cos B = A.i/|A| B is the angle with x axis Thanks Bharat Bajaj IIT Delhi...
  img
bharat bajaj 6 months ago
evaluate ∫ 2 cos^2 x- cos 2x / cos^2 x dx
 
 
Ans: Hello Student, Please find answer to your question below
  img
Jitender Singh 2 months ago
View all Questions »