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In triangle ABC, prove thattan(B-C)/2=(b...

In triangle ABC, prove that`tan(B-C)/2=(b-c)/(b+c)cotA/2``tan(C-A)/2=(c-a)/(c+a)cotB/2``tan(A-B)/2=(a-b)/(a+b)cotC/2`

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From sine law, we have, `a/sinA = b/sinB = c/sinC = k`
`:.a = ksinA, b = ksinB, c = ksinC`
`:.(b-c)/(b+c) = (k(sinB-sinC))/(k(sinB+sinC))`
`= (sinB - sinC)/(sinB+SinC)`
`= (2cos((B+C)/2)sin((B-C)/2))/(2sin((B+C)/2)cos((B-C)/2))`
` = cot((B+C)/2)tan((B-C)/2)`
Here, `A+B+C = 180`
...
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NCERT-TRIGONOMETRIC FUNCTIONS-SOLVED EXAMPLES
  1. If cotx=-5/(12), lies in second quadrant, find the values of other fi...

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  2. The minute hand of a watch is 1.5 cm long. How far does its tip move ...

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  3. If the arcs of the same lengths in two circles subtend angles 65 ^cir...

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  4. Convert 6 radians into degree measure.

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  5. Find the radius of the circle in which a central angle of 60^@interce...

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  6. Convert 40^circ 20^(prime)into radian measure.

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  7. Find the principal solution of the equation tanx=-1/(sqrt(3)).

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  8. Find the principal solution of the equation sinx=(sqrt(3))/2.

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  9. Find the value of sin\ 15^circ.

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  10. Prove that 3sinpi/6secpi/3-4sin(5pi)/6cotpi/4=1

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  11. Prove that (sin(x+y))/(sin(x-y))=(tanx+tany)/(tanx-tany)

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  12. Find the value of tan\ (13pi)/(12).

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  13. Prove that cos(pi/4+x)+cos(pi/4-x)=sqrt(2)cosx.

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  14. Show that tan 3x tan 2x tan x = tan 3x - tan 2x - tan x.

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  15. Prove that (sin5x-2sin3x+sinx)/(cos5x-cosx)=tanx

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  16. Prove that (cos7x+cos5x)/(sin7x-sin5x)=cotx.

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  17. In triangle ABC , prove that tan (B-C)/2 =[( b-c) /(b+c )] cot A/2 , ...

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  18. The angle of elevation of to be top point P of the vertical tower PQ o...

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  19. Prove that asin(B−C)+bsin(C−A)+csin(A−B)=0

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  20. In triangle ABC, prove thattan(B-C)/2=(b-c)/(b+c)cotA/2tan(C-A)/2=(c-a...

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