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Grade: 10
`        If sin4Θ/b + cos4Θ/a = (a+b)/ab , then prove that sin8Θ/a + cos8Θ/b = 1/(a3+b3)...`
5 months ago

## Answers : (2)

Arun
24489 Points
```							Let. theta.= x .The given question is as follows:-(sin^4 x)/a+(cos^4 x)/b = 1/(a+b). , prove that. (sin^8 x)/a^3 + (cos^8 x)/b^3= 1/(a+b)^3.(sin^4 x)/a +(cos ^4 x)/b= 1/(a+b)or. b.(sin^4 x) +a.(1-sin^2 x)^2= a.b/(a+b)or. b.sin^4 x+ a+a.sin^4 x-2a.sin^2 x= a.b/(a+b)or. (a+b).sin^4 x-2.a.sin^2x+a = a.b/(a+b)or. (a+b)^2.sin^4 x-2a(a+b).sin^2 x+a^2+ab=abor. {(a+b).sin^2 x}^2–2×(a+b).sin^2 x. × a. +(a)^2. = 0or. [(a+b).sin^2 x. - a. ]^2. = 0or. sin^2 x. = a/(a+b)……………..(1)or. [ sin^2 x]^4. = a^4/(a+b)^4.or. (sin^8 x)/a^3. = a/(a+b)^4……………(2)Now. cos^2 x= 1- sin^2x= 1- a/(a+b)cos^2 x= b/(a+b)…………………….(3)or. [cos^2 x]^4. = b^4/(a+b)^4or. (cos^8 x)/b^3. = b /(a+b)^4……………(4)Adding eqn.(2) and (4)(sin^8 x)/a^3+(cos^8 x)/b^3= (a+b)/(a+b)^4. = 1/(a+b)^3. Proved.
```
5 months ago
Vikas TU
11137 Points
```							Dear student Please follw this lnk https://www.askiitians.com/forums/Trigonometry/if-sin4a-a-cos4b-b-1-a-b-then-prove-that-sin_129529.htmGood Luck
```
5 months ago
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