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Prove that cos^2 48^@-sin^2 12^@=((sqrt5...

Prove that `cos^2 48^@-sin^2 12^@=((sqrt5+1))/8`

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UNITED BOOK HOUSE-ANNUAL EXAMINATION QUESTION PAPERS 2018-EXERCISE
  1. If AcapB^1=phi,then show that A=AcapBand hence show that AsubeB.

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  2. Find the domain and range of the real function f(x)=1/((1-x^2))

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  3. Prove that cos^2 48^@-sin^2 12^@=((sqrt5+1))/8

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  4. Show that cot 2x.cotx-cot3x.cot2x-cot3x.cotx=1

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  5. Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n) may be the ...

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  6. Find the value of r,if the coefficients of (2r+4)th and (r-2) -th term...

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  7. Find the principal amplitude of (-1-i).

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  8. Find the number of squares in chess board.

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  9. Find the focus of the parabola y=x^2+x+1.

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  10. Find the equation of a circle with centre (h,k)and touching both the ...

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  11. Evaluate lim(xrarrpi//6)(sqrt3sinx-cosx)/((x-pi/6))

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  12. Prove that the derivative of an odd function an ever function .

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  13. Find the mean and variance for each of the data in First n natural n...

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  14. If P(A)=2/3,P(B)=1/2,P(AcapB)=1/6,then find the value of P(AcapB')and ...

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  15. Let A={x in N:x^2-5x+6=0}.B={x in W:0lex<2}and C={x in N:x<3},then ver...

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  16. Prove that in any /\ABC.(b-c)cot(A/2)+(c-a)cot (B/2)+(a-b)cot (C/2)=0

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  17. Solve secx-tanx=sqrt3

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  18. If P-th ,q-th and r-th terms of an AP as well those of a GP are a,b,c ...

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  19. Using the principle of mathematical induction ,prove that x^n-y^nis di...

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  20. If z=x+iy andw=(1-iz)/(1+iz)such that |w|=1.then show that z is purely...

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