find the value of the following

Asked by sunil_0010 | 31st Oct, 2009, 08:56: PM

Expert Answer:

sin25+sin210+sin215+sin220+...........+sin285

= sin25 + sin210 + sin215 + sin220 + sin215+sin220 +  sin235+sin240 + sin245+sin2(90 - 40) + sin2(90 - 35) + sin2(90 - 30) +   sin2(90 - 25) + sin2(90 - 20)+ sin2(90 - 15) +sin2 (90 - 10)+ sin2(90 - 5)

Now, since sin (90 - θ) = cosθ

= sin25 + sin210 + sin215 + sin220 + sin215+sin220 +  sin235+sin240 + sin245+ cos240 + cos235 + cos2 30 +   cos2 25 + cos220 + cos215 + cos2 10 + cos25

= (sin25 + cos25) + (sin210 + cos2 10) + .............................................+ (sin240 + cos240) + sin245

Using the identity  sin2 θ + cos2θ = 1, we have

= 1 + 1+........(8 times) + (1/2)2

= 8 + 1/2

= 17/2

Answered by  | 5th Nov, 2009, 11:39: AM

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