Question

find the value of cos^2(5)+cos^2(10)+cos^2(15)+cos^2(20)........................+cos^2(180)
plz tell me fast. any one give me the correct answer these question is for genius only it​

Answer 1

Answer:

18

Step-by-step explanation:

We are given the series

cos25+cos210+cos215+…+cos2180

=cos25+cos210+cos215+…+cos2180

=cos25+cos210+cos215+…+cos285+cos290+cos295+...+cos2180

Using the identity cos(x)=sin(90−x) in the second part as follows we have,

=cos25+cos210+cos215+...+cos285+cos290+sin25+...+sin285+sin290

Using the identity cos2(x)+sin2(x)=1 we have,

=18 Since 18 such pairs are formed.(i.e., cos2(x)+sin2(x)=1 )

Therefore,

cos25+cos210+cos215+…+cos2180=18

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