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To prove (cos5x+cos4x)/(1-2cos3x)=-cos2x...

To prove `(cos5x+cos4x)/(1-2cos3x)`=`-cos2x-cosx`

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To prove the equation \[ \frac{\cos 5x + \cos 4x}{1 - 2\cos 3x} = -\cos 2x - \cos x, \] we will start with the left-hand side (LHS) and manipulate it to reach the right-hand side (RHS). ...
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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that: (1+cos4x)/(cot x-tanx)=1/2sin4x

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  2. Prove that: (cos7x-cos8x)/(1+2cos5x)=cos2x-cos3x

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  3. To prove (cos5x+cos4x)/(1-2cos3x)=-cos2x-cosx

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  4. If tantheta= t, then tan2theta+sec2theta is equal to (a) (1+t)...

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  5. Prove that: "cot"pi/(24)=sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)

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  6. (sec8A-1)/(sec4A-1) is equal to (A) (tan2A)/(tan8A) (B) (tan8A)/(t...

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  7. If A=2sin^2theta-cos2theta,t h e nA lies in the interval (a) [-1,3] (...

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  8. Prove that (tan3x)/(tanx) never lies between 1/3a n d3 .

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  9. The value of (cot (x/2)-t a n (x/2))^2(1-2tanxcot2x) is (a)1 (b) 2 (c)...

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  10. Prove that cos^3A+cos^3(120^0+A)+cos^3(240^0+A)=3/4cos3A

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  11. Simplify 2sin^2beta+4cos(alpha+beta)sinalphasinbeta+cos2(alpha+beta)

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  12. Prove that: "tan"pi/(16)=sqrt(4+2sqrt(2))-(sqrt(2)+1)

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  13. Prove that: "tan"142""(1^0)/2=2+sqrt(2)-sqrt(3)-sqrt(6)

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  14. Prove that:(sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

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  15. Prove that: (cosA+cosB)^2+(sinA-sinB)^2=4cos^2((A+B)/2) .

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  16. Prove that: (1+cos. (pi)/8)(1+cos. (3pi)/8)(1+cos. (5pi)/8)(1+cos. (7...

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  17. If sinA=3/5, where 0^0ltAlt90^0 , then find the values of sin2A , cos2...

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  18. Prove that: sin(pi/10) sin((13pi)/10)=-1/4

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  19. Show that: sqrt(2+sqrt(2+sqrt(2+2cos8theta)))=2costheta,0<theta<pi 8<=...

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  20. If tanalpha=1/7,sinbeta=1/(sqrt(10)), prove thatalpha+2beta=pi/4 , whe...

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