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

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

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To prove the identity \[ \frac{1 + \cos 4x}{\cot x - \tan x} = \frac{1}{2} \sin 4x, \] we will simplify the left-hand side step by step. ...
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RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. Prove that: sinpi/(10)+sin(13pi)/(10)=-1/2

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  2. If tan(pi//4+theta)+""tan(pi//4-theta)=lambdasec2theta,t h e m 3 (b)...

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

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

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

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  6. If tantheta=t t h e nt a n2theta+sec2theta is equal to (1+t)/(1-t) ...

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

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

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

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

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  11. The value of (cot (x/2)-t a n x/2)^2(1-2tanxcot2x) is 1 (b) 2 (c) 3 ...

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

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

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

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  15. Prove that tan7 1^circ/2 = sqrt6 - sqrt3 + sqrt2 - 2.

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

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

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  18. Prove that: (1+cospi/8)(1+cos(3pi)/8)(1+cos(5pi)/8)(1+cos(7pi)/8)=1/8

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

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  20. Find the value of sin(pi/10) sin((13pi)/10)

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