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If a,b,c are in HP, then prove that sin ...

If a,b,c are in HP, then prove that `sin ^(2) ""(A)/(2), sin ^(2) ""(B)/(2), sin ^(2) ""(C )/(2)` are also in HP.

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The correct Answer is:
`=(ab)/((s-a)(s-b))+(bc)/((s-b)(s-c))=RHS`
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ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If a,b,c are in HP, then prove that sin ^(2) ""(A)/(2), sin ^(2) ""(B)...

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  2. In a triangle XYZ, let x, y, z be the lengths of sides opposite to the...

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  3. In a triangle the sum of two sides is x and the product of the same is...

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  4. Consider a triangle A B C and let a , ba n dc denote the lengths of th...

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  5. In a triangle PQR, P is the largest angle and cosP=1/3. Further the in...

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  6. Let PQR be a triangle of area Delta with a = 2, b = 7/2 and c =5/2, wh...

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  7. If the angle A ,Ba n dC of a triangle are in an arithmetic propression...

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  8. Let A B C be a triangle such that /A C B=pi/6 and let a , ba n dc deno...

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  9. a triangle A B C with fixed base B C , the vertex A moves such that co...

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  10. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

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  11. A straight line through the vertex P of a triangle PQR intersects the ...

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  12. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  13. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  14. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  15. Internal bisector of /A of triangle ABC meets side BC at D. A line dra...

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  16. Given an isosceles triangle, whose one angle is-2pi/3 and the radius o...

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  17. In Delta ABC, which one is true among the following ?

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  18. Let a vertical tower A b have its end A on the level ground. Let C be ...

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  19. ABCD is a trapezium such that AB and CD are parallel and BC | CD. If ...

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  20. For a regular polygon, let r and R be the radii of the inscribed and ...

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  21. In triangle A B C , let /c=pi/2dot If r is the inradius and R is circu...

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