sin4A/a + cos4A/b = 1/(a+b)what is the value sin8A/a3 + cos8A/b3
sin4A/a + cos4A/b = 1/(a+b)
what is the value sin8A/a3 + cos8A/b3
kalpesh , 8 Years ago
Grade 12
Trigonometry> sin 4 A/a + cos 4 A/b = 1/(a+b) what is t...
1 Answers
Arun
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
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
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.
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: 3 Years ago
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
trigonometry
1 Answer Available
Last Activity: 3 Years ago
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
1 Answer Available
Last Activity: 3 Years ago
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
1 Answer Available
Last Activity: 4 Years ago
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥
trigonometry
1 Answer Available
Last Activity: 4 Years ago