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Show that sin^2(x+alpha)+sin^2(x+beta)-2...

Show that `sin^2(x+alpha)+sin^2(x+beta)-2cos(alpha-beta).sin(x+alpha)sin(x+beta)`is independatn of x.

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UNITED BOOK HOUSE-TAKI HOUSE-EXERCISE
  1. If alphaand beta be two roots of the equation (x-a)(x-b)=c then show t...

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  2. Evaluate :cos^2(pi/8)+cos^2((3pi)/8)+cos^2((5pi)/8)+cos^2((7pi)/8)

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  3. If cosalpha+cosbeta=2/3and sinalpha+sinbeta=2/5then find the vvalue of...

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  4. If cosec theta+sectheta=cosecalpha+secalpha,then show that tan ((theta...

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  5. x=2cost+3y=2sint+5 and t=parameter find the locus of the point (x,y)

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  6. Find the equations of a straight line parallel to x-axis and passes th...

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  7. Prove by mathematical induction ,3^(2n+1)+2^(n+2)is divisible by 7,n i...

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  8. Factorise:x^2+y^2+z^2-xy-yz-zx

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  9. Solve :2y^2+3y+8-6i=0

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  10. The sum of first three terms of an arithmetic progression with n terms...

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  11. Show that sqrt3/(sin20^@)-1/(cos20^@)=4

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  12. If tan(alpha+beta)=a+b and tan(alpha-beta)=a-b then show that atanalph...

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  13. Show that,tan7 (1^@/2)=sqrt6-sqrt3+sqrt2-2

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  14. Show that the area of the triangle formed by the lines y = m(1) x + c(...

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  15. Find the co-ordinate of the orthocentre of a triangle whose vertices a...

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  16. If arg ((z-1)/(z+1))=pi/4,, then show that in complex plane, the locus...

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  17. Find the sum of n terms of 12+105+1008+10011+….

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  18. Show that sin^2(x+alpha)+sin^2(x+beta)-2cos(alpha-beta).sin(x+alpha)si...

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  19. If cosalpha=x/(y+z),cosbeta=y/(z+x)and cosgamma=z/(x+y)then show that ...

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  20. A variable straight line passes through the point of intersection of t...

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