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If costheta=1/2(a+1/a),cos3theta=lambda(...

If `costheta=1/2(a+1/a),cos3theta=lambda(a^3+1/(a^3)),t h e nlambda=` (a)`-1/4` (b) `1/4` (c) 1 (d) none of these

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`costheta=1/2(a+1/a)`
`cos3theta=lambda(a^3+1/(a^3))`
`=costheta(4cos^2theta-3)`
`=1/2(a+1/a)(4(1/2(a+1/a))^2-3)`
`=1/2(a+1/a)(a^2+1/(a^2)+2-3)`
`=1/2(a+1/a))(a^2+1/(a^2)-1)`
`=1/2(a^3+1/a-a+a+1/(a^3)-1/a)`
...
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RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
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  2. The value of (sin5alpha-sin3alpha)/(cos5alpha+2cos4alpha+cos3alpha) is

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  3. If costheta=1/2(a+1/a),cos3theta=lambda(a^3+1/(a^3)),t h e nlambda= ...

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  4. Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3A

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  5. If t a n^2theta=2tan^2phi+1 , prove that cos2theta+sin^2phi=0.

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  6. If theta=pi/(2^n+1) , prove that: 2^ncosthetacos2thetacos2^2 cos2^(n-1...

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  7. Prove that: cotA+"cot"(60^0+A)-cot(60^0-A)=3cot3A

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  8. Prove that: cos^2 48^0-sin^2 12^0=(sqrt(5)+1)/8

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  9. Find sin x/2 ,cos x/2 and tan x/2 of the following : tanx=-4/3,""x in...

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  10. Find the values of cospi/8

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  11. Prove that: sin(pi/14)sin((3pi)/14)sin((5pi)/14)sin((7pi)/14)sin((9pi...

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  12. Prove that: (1+sec2theta)(1+sec4theta)(1+sec8theta)(1+sec2^ntheta)=t a...

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  13. If theta=pi/(2^n+1) , prove that: 2^ncosthetacos2thetacos2^2 cos2^(n-1...

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  14. Prove that: cos(pi/7)cos((2pi)/7)cos((4pi)/7)=-1/8,

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  15. If alpha and beta are distict roots of acostheta+b sintheta=c , prov...

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  16. sin^2(A/2+pi/8) - sin^2(A/2-pi/8)= 1/sqrt(2)sinA

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  17. Sin 4A = 4 cos^3 A sin A - 4 sin^3 A cos A

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  18. If tanA=1/7a n dtanB=1/3 , show that cos2A=sin4Bdot

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  19. If 2t a nalpha/2=tan(beta/2) , prove that cosalpha=(3+5cosbeta)/(5+3c...

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  20. If acos2theta+bsin2theta=ch a salphaa n dbeta as its roots , then prov...

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