sin4A/a + cos4A/b = 1/(a+b)what is the value sin8A/a3 + cos8A/b3
kalpesh , 6 Years ago
Grade 12
Trigonometry> sin 4 A/a + cos 4 A/b = 1/(a+b) what is t...
1 Answers
Arun
Last Activity: 6 Years ago
cos^4x=(cos^2x)^2=(1-sin^2x)^2=1+ sin^4x-2sin^2x
=>sin^4x / a +cos^4x / b=1/a+b
=>sin^4x/a + (1+sin^4x-2sin^2x)/b = 1/(a+b)
[b*sin^4x + a(sin^4x-2sin^2x+1)] /ab = 1/(a+b)
=>[(a+b)sin^4x-2a sin^2x+a]/ab = 1/a+b
=>(a+b)^2 sin^4x - 2a(a+b)sin^2x + a(a+b) =ab
=>(a+b)^2 sin^4x - 2a(a+b)sin^2x + a^2
=> [(a+b)sin^2x-a]^2 = 0
=>(a+b)sin^2x - a = 0
sin^2x=a/(a+b).........(1)
(take fourth power of both side)
=>sin^8x=a^4/(a+b)^4
(divide by a^3 both side)
=>sin^8x/a^3=a/(a+b)^4.
........(2)
=>cos^2x=1 - sin^2x=1-a/(a+b)=b/(a+b). (from eq 1 substituting value of sin^2x)
=>cos^2x=b/(a+b)...........(3)
(take fourth power of both side)
=>cos^8x=b^4/(a+b)^4
(divide by b^3 both side)
=>cos^8x/b^3 =b/(a+b)^4......(4)
(adding eq 2@4)
=>sin^8x/a^3 + cos^8x/b^3=a/(a+b)^4 + b/(a+b)^4 =(a+b)/(a+b)^4=1/(a+b)^3
=>sin^4x / a +cos^4x / b=1/a+b
=>sin^4x/a + (1+sin^4x-2sin^2x)/b = 1/(a+b)
[b*sin^4x + a(sin^4x-2sin^2x+1)] /ab = 1/(a+b)
=>[(a+b)sin^4x-2a sin^2x+a]/ab = 1/a+b
=>(a+b)^2 sin^4x - 2a(a+b)sin^2x + a(a+b) =ab
=>(a+b)^2 sin^4x - 2a(a+b)sin^2x + a^2
=> [(a+b)sin^2x-a]^2 = 0
=>(a+b)sin^2x - a = 0
sin^2x=a/(a+b).........(1)
(take fourth power of both side)
=>sin^8x=a^4/(a+b)^4
(divide by a^3 both side)
=>sin^8x/a^3=a/(a+b)^4.
........(2)
=>cos^2x=1 - sin^2x=1-a/(a+b)=b/(a+b). (from eq 1 substituting value of sin^2x)
=>cos^2x=b/(a+b)...........(3)
(take fourth power of both side)
=>cos^8x=b^4/(a+b)^4
(divide by b^3 both side)
=>cos^8x/b^3 =b/(a+b)^4......(4)
(adding eq 2@4)
=>sin^8x/a^3 + cos^8x/b^3=a/(a+b)^4 + b/(a+b)^4 =(a+b)/(a+b)^4=1/(a+b)^3
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on Trigonometry
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: 2 Year ago(s)
\tFind the general solution of equation tan3∂=cot2∂For all angles between -720 and +720
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)
cos^2 13ºcos^2 47º+cos^2 73º =? …..................
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)