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AP EAMCET202316 May 2023Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If A+ (A+B)+ (A+2 B)+ upto n terms = ( 2 ~A +( n -1) B 2 ) nB 2 cosec B 2 , then 19 + 3 19 + 5 19 + + 17 19 =

Options

  1. A1
  2. B- 1 2
  3. C1 2
  4. D0

Correct answer

C. 1 2

Step-by-step solution

Given, A+ (A+B)+ (A+2 B)+ upto n terms = ( 2 A+(n-1) B 2 ) n B 2 cosec B 2 Now, 19 + 3 19 + ( 5 19 )+ + 17 19 aligned = ( 19 )+ ( 19 + 2 19 )+ ( & . 19 +2 2 19 ) & + + ( 19 +8 2 19 ) aligned array r = ( 2 19 +8 2 19 2 ) ( 9 2 2 19 ) cosec ( 2 2 19 ) here A= 19 , B= 2 19 and n=9 array aligned & = ( 9 19 ) ( 9 19 ) cosec ( 2 19 ) & = 1 2 ( 18 19 ) cosec ( 19 )= 1 2 ( - 19 ) cosec ( 19 ) & = 1 2 ( 19 ) cosec ( 19 )= 1 2 1= 1 2 aligned

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