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a cos ^(2) "" ( A) /(2) + b cos ^(2) ""...

` a cos ^(2) "" ( A) /(2) + b cos ^(2) "" ( B)/(2) = c cos ^(2) "" ( C) /(2) =`

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Find b cos ^(2) ""( C ) /(2) + c cos ^(2) "" ( B ) /(2 )

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If a cos ^(2) "" (C )/(2) +c cos ^(2) "" (A)/(2) = (3b)/( 2 ) " then " a,b,c are in

If A, B , C =pi, then prove that cos ^(2). (A)/(2)+ cos^(2). (C)/(2)- cos^(2). (C)/(2)=2(cos. (A)/(2) cos. (B)/(2)sin. (C)/(2))

If A+B+ C =pi , then prove that cos ^(2) (A/2)+ cos ^(2) (B/2) +cos ^(2) (C/2)=2(1+sin . (A)/(2) sin. (B)/(2) sin. (C)/(2))

In DeltaABC , " find " b cos ^(2).(C)/(2)+c cos^(2).(B)/(2)

AAKASH SERIES-PROPERTIES OF TRIANGLES-EXERCISE - 9.1 ( LONG ANSWER QUESTIONS)
  1. In DeltaABC" show that "suma^(3)cos(B-C)=3abc

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  2. a^(2) cot A + b^(2) cot B + c^(2) cot C "" ( abc)/( R)

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  3. a cos ^(2) "" ( A) /(2) + b cos ^(2) "" ( B)/(2) = c cos ^(2) "" ( C...

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  4. b^(2) sin 2C + C^(2) sin 2B = 2 b sin A

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  5. In a /\ABC if a^(2)+b^(2)+c^(2)=8R^(2) then show that/\ABC is a right ...

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  6. If cos ^(2) A + cos ^(2) B = cos ^(2) C = 1 then show that Delta A...

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  7. If cot.(A)/(2)=(b+c)/(a) find angle B

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  8. Show that cot ""(A)/(2) + cot "" ( B)/(2) + cot "" ( C ) /(2)...

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  9. In DeltaABC,(cot(A//2)+cot(B//2)+cot(C//2))/(cotA+cotB+cotC)=

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  10. Prove that tan.(A)/(2)+tan.(B)/(2)+tan.(C)/(2)=(bc+ca+ab-s^(2))/(Delta...

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  11. In DeltaABC show that (a+b+c)(tan.(A)/(2)+tan.(B)/(2))=2cot.(C)/(2)

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  12. If sin theta = a/(b+c) then show that cos theta = (2sqrt(bc))/(b+c) co...

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  13. If a = (b-c) "sec" theta, then prove that tan theta = (2sqrt(bc))/(b-c...

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  14. If cot.(A)/(2)+cot.(B)/(2)+cot.(C)/(2) are in A.P , then prove that a,...

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  15. If tan ""(A)/(2) = (5)/(6) , tan "" (B)/(2) = ( 20 )/( 37) then s...

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  16. If cot A/2:cot"" B/2: cot"" C/2 = 3:5:7 then show that a:b:c = 6:5:4.

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  17. IF p1,p2,p3 are the lengths of the altitudes of a triangle from the ve...

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  18. If p1 , p2 , p3 are the altitudes drawn from the vertices A,B, C of ...

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  19. Two ships leave a port at the same time . One goes 24km per hour in th...

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  20. A tree stands vertically on the slant of the hills From a point A on t...

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