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Solve: costheta+cos3theta+cos5theta+cos7...

Solve: `costheta+cos3theta+cos5theta+cos7theta=0`

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We have `costheta+cos7theta+cos3theta+cos5theta=0`
`rArr 2cos4thetacos3theta+2cos4thetacostheta=0 rArr cos4theta(cos3theta+costheta)=0`
`rArr` Either `costheta=0 rArr theta=(2n_(1)+1)pi//2, n_(1) in I`
or `cos2theta=0 rArr theta=(2n_(2)+1)pi/4, n_(2) in I`
or `cos4theta=0 rArr theta=(2n_(3)+1)pi/8, n_(3) in I` Ans.
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ALLEN-BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -EXERCISE (S-1)
  1. Solve: costheta+cos3theta+cos5theta+cos7theta=0

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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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  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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  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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  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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