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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 cos 2a=2sin^(2)beta+4cos (alpha+beta)sin alpha sin beta+cos...

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  2. Prove that: s in^4pi/8+s in^4(3pi)/8+s in^4(5pi)/8+s in^4(7pi)/8=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. If tan.(pi)/(24)=(sqrt(p)-sqrt(q))(sqrt(r )-s), then the value of p+q+...

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  5. If m tan (theta - 30^(@))= n tan (theta + 120^(@)), show that cos 2 th...

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  6. It cos(alpha+beta)=4/5,sin(alpha-beta)=5/(13)a n dalpha,beta lie betwe...

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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)/7dotcospi/7-1=2cos(2pi)/7dot

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

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

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

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  14. Prove that from the equality (sin^(4)alpha)/a+(cos^(4)alpha)/b=1/(a+b)...

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

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  16. The value of (cotθ+cosecθ-1)/ (cotθ-cosecθ+1) is

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

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

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

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  20. Find values of theta satisfying sintheta+sin5theta=sin3theta such that...

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