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

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

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To prove the equation \[ \frac{\cos 7x - \cos 8x}{1 + 2\cos 5x} = \cos 2x - \cos 3x, \] we will follow a systematic approach using trigonometric identities. ...
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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. If tan(pi//4+theta)+""tan(pi//4-theta)=lambdasec2theta,t h e nlambda= ...

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  2. Prove that: (1+cos4x)/(cot x-tanx)=1/2sin4x

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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