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If x=sin(theta+(7pi)/(12))+sin(theta+pi/...

If `x=sin(theta+(7pi)/(12))+sin(theta+pi/(12))+sin(theta+(3pi)/(12))dot` `Y=cos(theta+(7pi)/(12))+cos(theta+pi/(12))+cos(theta+(3pi)/(12))dot` then prove that `X/Y-Y/X=2tan2theta`

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ALLEN-BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -EXERCISE (S-1)
  1. Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + co...

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  2. sin^4(pi/16)+sin^4(3pi/16)+sin^4(5pi/16)+sin^4(7pi/16)=3/2

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  3. If x=sin(theta+(7pi)/(12))+sin(theta+pi/(12))+sin(theta+(3pi)/(12))dot...

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  4. 6. Find the positive integers p, q, r, s satisfying tan (pi/24)=(sqrt(...

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  5. if m*tan(theta-30)=n*tan(theta+120), show that cos2theta=(m+n)/(2(m-n)...

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  6. If cos(alpha+beta)=4/5; sin(alpha-beta)=5/13 and alpha,beta lie betwee...

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  7. If the value of the expression sin 25^@* sin 35^@* sin 85^@ can be exp...

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  8. Prove that (4cos^2 9^0-3)(4cos^2 27^0-3)=tan9^0dot

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  9. Prove that 4cos((2pi)/7).cos(pi/7)-1=2cos((2pi)/7).

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  10. Let P(k)=(1+cospi/(4k)) (1+cos((2k-1)pi)/(4k)) (1+cos((2k+1)pi)/(4k))...

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  11. Calculate without using trigonometric tables: (a) 4 cos 20^@ - sqrt3 c...

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  12. (2cos4 0^(@)-cos2 0^(@))/(sin2 0^(@)

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  13. cos^6(pi/16)+cos^6(3pi/16)+cos^6(5pi/16)+cos^6(7pi/16)

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  14. tan1 0^(@)-tan5 0^(@)+tan7 0^(@)

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  15. Given that (1+tan1^@)(1+tan2^@)+...........+(1+tan45^@)= 2^n find n .

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  16. If a leq 3 cos (theta+pi/3)+5cos theta+3 leq b, find a and b, where ...

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  17. Let k=1^@ then prove that sum(n=0)^(88)1/(cosnkcos(n+1)k)=cosk/sin^2k

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  18. If x and y are real number such that x^2 +2xy-y^2=6, find the minimum...

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  19. If A+B+C=pi, prove that tan^2A/2+tan^2B/2+tan^2C/2geq1.

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  20. solve the equation for x , 5^(1/2)+5^(1/2 + log5 sinx) = 15^(1/2 + log...

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