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Prove that :cot(A-B)cot(B-c)+cot(B-c)cot...

Prove that :cot(A-B)cot(B-c)+cot(B-c)cot(C-A)+cot(A-B)cot(B-C)=1

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In any triangle prove that cot(A/2)+cot (B/2)+cot(C/2)=cot(A/2)cot(B/2)cot(C/2)

For any triangle ABC prove that (b-c)cot(A/2)+(c-a)cot(B/2)+(a-b)cot(C/2) =0

Prove that cot12^(@)cot38^(@)cot52^(@)cot78^(@)cot60^(@)=(1)/(sqrt3)

Prove that (b + c -a) (cot.(B)/(2) + cot.(C)/(2)) = 2a cot.(A)/(2)

Show that, cot16^(@) cot44^(@) + cot44^(@) cot76^(@) + cot76^(@) cot 16^(@) = 3

If the sides a,b,c of a triangle ABC are in A.P., prove that cosA "cot" (A)/(2) , cosB "cot" (B)/(2), cosC "cot" (C)/(2) are also in A.P.

Prove that "cot"(pi)/(8)"cot"(3pi)/(8)"cot"(5pi)/(8)"cot"(7pi)/(8)=1.

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

cot ^(-1)x+cot^(-1)(a^(2)-x+1)=cot ^(-1)(a-1)

In any triangle ABC, prove that, (b-c)cot 'A/2' + (c-a) cot 'B/2' + (a-b) cot 'C/2'=0

UNITED BOOK HOUSE-BETHUNE COLLEGIATE SCHOOL.-EXERCISE
  1. Prove that (1+sec2A)(1+sec2^2A)(1+sec2^3A).....(1+sec2^nA)=(tan2^nA)/(...

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  2. Prove that ,tan(alpha+beta)tan(alpha-beta)=(sin^2alpha-sin^2beta)/(cos...

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  3. How many 5 digit numbers can be formed using the digits 0,2,5,6,7 with...

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  4. Show that ,((1+i)/(1-i))^2+((1-i)/(1+i))^2is a real number.

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  5. Find the distance between the lines 3x+4y=9 and 6x+8y+15=0.

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  6. Find the value of :lim(xrarr0)(sin2x+sin6x)/(sin5x-sin3x)

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  7. In an examination 60% passed in mathematics,68% passes in statistics a...

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  8. If alpha!=betaand atanalpha+b tanbeta=(a+b)tan((alpha+beta)/2),then sh...

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  9. For any three sets A,Band C show that :Acap(BcupC)=(AcapB)cup(AcapC)

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  10. Prove using principle of mathematical induction that sum of the cube t...

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  11. If w be a imaginary cube root of uniyt and a+b+c=0 then show that (a+b...

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  12. Find the sum upto n terms of the following series 4+44+444+….n.

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  13. Show that the straight lines 5x-y=6,x+5y-22=0,5x-y-32=0 and x+5y+4=0 f...

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  14. Find the value of :lim(xrarra)(xsina-asinx)/(x-a)

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  15. Prove that :cot(A-B)cot(B-c)+cot(B-c)cot(C-A)+cot(A-B)cot(B-C)=1

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  16. Provethat: (cos3theta)/(sin2thetasin4theta)+(cos5theta)/(sin4thetasin6...

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  17. Two parallel straight lines contains 5 points and 10 points respective...

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  18. Find the sum of the following series (1)+(2+3)+(4+5+6)+(7+8+9+10)+…to ...

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  19. If ab+bc+ca=0 then prove that the straight lines x/a+y/b=1/c,x/b+y/c=1...

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  20. Evaluate lim(xrarrpi//4)(4sqrt2-(cosx+sinx)^5)/(1-sin2x)

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