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If alphaand betaare positive acute angle...

If `alpha`and `beta`are positive acute angles and `cos2alpha=(3cos2beta-1)/(3-cos2beta)`,then prove that `tan alpha=sqrt2tanbeta`

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UNITED BOOK HOUSE-ANNUAL EXAMINATION QUESTION PAPERS 2014-EXERCISE
  1. Find the mean deviation about the mean for the following data:39,51,59...

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  2. For any two sets A and B, A-(A-B) equals

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  3. If alphaand betaare positive acute angles and cos2alpha=(3cos2beta-1)/...

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  4. Solve for x:cos^3xsin3x+sin^3xcos3x=3/4

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  5. Prove that by using the principle of mathematical induction for all n...

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  6. If z=x+iy and |2z+1|=|z-2i|,then prove that 3(x^2+y^2)+4(x+y)=3

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  7. Out of 14 articles,10 are of same type and each of the remaining is of...

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  8. In the expansion of (root(3)(2)+1/root(3)(3))^nthe rationof the 7th te...

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  9. If the sum of sirst n terms of a G.P is p.sum of its first 2n terms is...

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  10. The equations of two sides of a square are 5x+12y-10=0 and 5x+12y+29=0...

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  11. If the straight line x/a+y/b=1is parallel to the line 4x+3y=6 and pas...

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  12. Find the equations of the circles which pass through the origin and cu...

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  13. Evaluate:lim(xrarr0)(sin(x^2+4x))/(x^3-5x^2+2x)

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  14. Find from the first principle,the derivative of tan 2x at x=pi/8

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  15. Show that the following statement is true by the method of contraposit...

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  16. Prove the following by contradiciton ."The sum of a rational and an ir...

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  17. What is the probability that a year,selected at random,in between 2001...

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  18. For a group of 200 students the mean and S.D of marks obtained by them...

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  19. Prove thatcos^2alpha+cos^2(120^@-alpha)+cos^2(120^@+alpha)=3/2

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  20. Prove that tan70^(@)=2tan50^(@)+tan20^(@).

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