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Question

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

+sin285+sin290 is equal to


A

7

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B

8

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C

9

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D

192

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Solution

The correct option is

D

192



Given expression is

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

We know that sin90=1 or sin290=1

The angles are in A.P. with common difference 5 and has 18 terms. We also know that sin285=[sin(905)]2=cos25.

Therefore from the complementary rule, we find sin25+sin285=sin25+cos25=1
Similarly, for sin210+sin280=sin210+sin2(9010)
=sin210+cos210=1
So, all we can arrange all terms in pair wise except the middle terms sin245 and last term sin90 and its values are sin245=12 and sin290=1

Therefore, sin25+sin210+sin215+.............+sin285+sin290

=(1+1+1+1+1+1+1+1)+1+12=912=192.


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