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If x costheta+ysintheta=xcosphi+ysinphit...

If `x costheta+ysintheta=xcosphi+ysinphi`then show that `y=x tan ((theta+phi)/2)`

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If (x-a)costheta+ysintheta=(x-a)cosphi+ysinphi=a and tan(theta/2)-tan(phi/2)=2b ,then (a) y^2=2a x-(1-b^2)x^2 (b) tan(theta/2)=1/x(y+b x) (c) y^2=2b x-(1-a^2)x^2 (d) tan(phi/2)=1/x(y-b x)

If cos theta=(acosphi+b)/(a+bcosphi)(theta,phiacute angle) show that tan(theta/2)=sqrt((a-b)/(a+b))tan (phi/2)(a>b)

If x+iy=3/(2+costheta+i sintheta) then show that x^2 + y^2 = 4x - 3.

If sin theta + sin phi = a, cos theta + cos phi = b prove that tan ((theta-phi)/2 )=pm sqrt((4-a^(2)-b^(2))/(a^(2)+b^(2)))

If cos theta = n cos ( theta + 2 phi) "show that"(n+1) tan ( theta + phi)= (n-1) cot phi

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sintheta+sinphi=a,costheta+cosphi=b show that tan((theta-phi)/2)=+-sqrt((4-a^2-b^2)/(a^2+b^2))

If " "a cos phi = b cos theta," show that " a tan theta + b tan phi = (a+b) tan ((theta + phi)/2)

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UNITED BOOK HOUSE-TIRTHAPATI INSTITUTION -EXERCISE
  1. If AsubeBand BsubeCthen show that AsubeC.

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  2. Show that (cos2^@-sin2^@)/(cos2^@+sin2^@)=tan43^@

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  3. If x costheta+ysintheta=xcosphi+ysinphithen show that y=x tan ((theta+...

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  4. IF 2 costheta=x+1/xthen show that 2 cos3 theta=x^3+1/x^3

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  5. Find the value of sin (221//2^@) with the help of the value of cos45^@

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  6. tan25^@=a prove that (tan155^@-tan115^@)/(1+tan155^@.tan115^@)=(1-a^2)...

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  7. Prove that,cos(pi/5)-cos((2pi)/5)=1/2

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  8. By the principle of mathematical induction prove that (5^(2n)-1)is alw...

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  9. IF x=a+bw+cw^2,y=a+bw^2+cwthen show that x^3+y^3=(2a-b-c)(2b-c-a)(2c-a...

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  10. If the roots of the quadratic equation a(b-c)x^2+b(c-a)+c(a-b)=0be eq...

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  11. Prove that (AcupB)^c=A^c capB^c[without venn-diagram]

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  12. If sinx-siny=a and cosx+cosy=b,prove that tan((x+y)/2)=+-sqrt((4-a^2-b...

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  13. Mathematically find the value of sin18^@

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  14. Show that cos(pi/11)cos((2pi)/11)cos((3pi)/11)cos((4pi)/11)cos((5pi)/1...

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  15. If cosx+cosy+cosz=0and sinx+siny+sinz=0then show that cos(x-y)+cos(y-z...

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  16. If z=x+iy and |2z-1| =|z-2|then prove that x^2+y^2=1

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  17. If the two roots of the quadratic equation ax^2+bx+c=0and alphaand bet...

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  18. For any three sets A,B,C prove by the formulae of set algebra that (Ac...

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  19. By the principle of mathematical induction prove that 1+2+3+4+…n=(n(n+...

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  20. Prove that tan1^@tan2^@tan3^@...tan88^@tan89^@=1

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