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Question

The value of sin25+sin210+sin215 + ..............+

sin285+sin290 is equal to


  1. 7

  2. 8

  3. 9

  4. 9 12


Solution

The correct option is D

9 12


Given expression is

sin25+sin210+sin215+..............+sin285+sin290

We know that sin90=1 or sin290=1

Similarly, sin45=12 or sin245=12 and the angles are in A.P. of 18 terms. We also know that

sin285=[sin(905)]2=cos25

 From the complementary rule, we find~sin25+sin285=sin25+cos25=1

sin25+sin210+sin215+.............+sin285+sin290

 =(1+1+1+1+1+1+1+1)+1+12=912

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