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In A B C , prove that (a-b^2cos^2C/2+(a...

In ` A B C ,` prove that `(a-b^2cos^2C/2+(a+b)^2sin^2C/2=c^2dot`

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LHS
`(a-b)^2cos^2 (C/2)+(a+b)^2sin^2 (C/2)`
`(a^2+b^2-2ab)cos^2(C/2)+(a^2+b^2+2ab)sin^2(C/2)`
`(a^2+b^2)[cos^2(C/2)+sin^2(C/2)]-2ab(cos^2(C/2)-sin^2(C/2))`
`a^2+b^2-2ab(cos^2(C/2)-sin^2(C/2))`
`a^2+b^2+2ab(sin^2(C/2)-cos^2(C/2))`
`a^2+b^2-2ab(cosc)`
`a^2+b^2-2ab((a^2+b^2-c^2)/(2ab))`
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CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. In A B C ,= if (a+b+c)(a-b+c)=3a c , then find /Bdot

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  2. In A B C , prove that (a-b^2cos^2C/2+(a+b)^2sin^2C/2=c^2dot

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  3. If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in ...

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  4. If a=sqrt(3),b=1/2(sqrt(6)+sqrt(2))dot and c=2, then find /A

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  5. In a scalene triangle A B C ,D is a point on the side A B such that C ...

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  6. In a "DeltaA B C"," "/"C"=60" "&\ /A=75. If D is a point on A C such t...

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  7. In a triangle A B C ,/A=60^0a n db : e=(sqrt(3)+1):2, then find the va...

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  8. A tower subtends angles alpha,2alpha,3alpha respectively, at point A ,...

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  9. In a triangle, if the angles A , B ,a n dC are in A.P. show that 2cos1...

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  10. If in a triangle A B C ,/C=60^0, then prove that 1/(a+c)+1/(b+c)=3/(a+...

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  11. Perpendiculars are drawn from the angles A, B and C of an acute-angled...

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  12. If pa n dq are perpendicular from the angular points A and B of A B C...

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  13. The two adjacent sides of a cyclic quadrilateral are 2a n d5 and the a...

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  14. In a circle of radius r , chords of length a and b cm subtend angles t...

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  15. In A B C , as semicircle is inscribed, which lies on the side cdot If...

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  16. In any /\ A B C , prove that (b^2-c^2)cotA+(c^2-a^2)cotB+(c^a-b^2)cot...

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  17. In triangle ABC, angle A is greater than angle B. If the measure of an...

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  18. In triangle A B C ,a : b : c=4:5: 6. The ratio of the radius of the ci...

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  19. The set of all real numbers a such that a^2+2a ,2a+3,a n da^2+3a+8 are...

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  20. A polygon of nine sides, each side of length 2, is inscribed in a c...

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