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Solve the equation sin^(4)x + cos^(4)x =...

Solve the equation `sin^(4)x + cos^(4)x =7/2 sinx.cosx.`

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`sin^(4)x+cos^(4)x=7/2sinx.cosx rArr (sin^(2)x +cos^(2)x)^(2) =7/2sinx.cosx`
`rArr 1-1/2(sin2x)^(2)=7/4(sin2x) rArr 2sin^(2)2x+7sin2x-4=0`
`rArr (2sin2x-1)(sin2x+4) =0 rArr sin2x =1/2` or `sin2x = -4` (Which is not possible) `rArr 2x = npi+(-1)^(n)pi/6 , n in I`
i.e, `x=(npi)/(2)+(-1)^(n)pi/12, n in I` Ans.
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ALLEN-BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -EXERCISE (S-1)
  1. Solve the equation sin^(4)x + cos^(4)x =7/2 sinx.cosx.

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  2. Solve the following equations where x in R a) (x-1)|x^(2)-4x+3|+2x^(...

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  3. Consider the function f(x) =|x-1|-2|x+2|+|x+3|

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  4. Find the square of the sum of the roots of the equation log(3)x.log(...

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  5. Find the value of 49^(1-log(7)2)+5^(-log(5)4)

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  6. if a,b,c are positive real numbers such that a^(log3(7));b^(log7(11))=...

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  7. Solve for x: a) (log(10)(x-3))/(log(10)(x^(2)-21)) = 1/2 b) log(lo...

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  8. If x,y>0 logy x+logx y=10/3 and xy=144 then (x+y)/2=sqrtN where N is a...

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  9. Solve the system of equations: (log)a x(log)a(x y z)=48(log)a y loga(x...

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  10. Solve the equation for x:x^(logx+4) = 32, where base of logarithim is ...

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  11. Find the product of the positive roots of the equation sqrt((2008))...

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  12. Solve the inequality: log(1//2)(x+1) gt log(2)(2-x)

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  13. Solve the inequality: log(x)2.log(2x)2. log(2)4x gt 1

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  14. Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+be...

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  15. Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + co...

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  16. sin^4(pi/16)+sin^4(3pi/16)+sin^4(5pi/16)+sin^4(7pi/16)=3/2

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  17. If x=sin(theta+(7pi)/(12))+sin(theta+pi/(12))+sin(theta+(3pi)/(12))dot...

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  18. 6. Find the positive integers p, q, r, s satisfying tan (pi/24)=(sqrt(...

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  19. if m*tan(theta-30)=n*tan(theta+120), show that cos2theta=(m+n)/(2(m-n)...

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  20. If cos(alpha+beta)=4/5; sin(alpha-beta)=5/13 and alpha,beta lie betwee...

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  21. If the value of the expression sin 25^@* sin 35^@* sin 85^@ can be exp...

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