Question

cos^2 5 degree + cos ^2 10 degree =

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Answer 1

Answer:

Step-by-step explanation:

= cos25+cos210+cos215......cos275+cos280+cos285+cos290

 

Now cos90= 0, putting the value we get

 

= cos25+cos210+cos215......cos275+cos280+cos285

 

= (cos25+cos285)+(cos210+cos280)+(cos215+cos285)+....+(cos240+cos250)+cos245

 

Now put cos?=sin(90-?), replacing this we get

 

= (cos25+sin25)+(cos210+sin210)+(cos215+sin215)+....+(cos240+sin240)+cos245

 

Total number of terms in the equation initially were 90/5 = 18

cos 90 was zero so remaining terms were 17, cos 45 is separate so remaining terms  

are 16 which are grouped in group of 2 so means 8 groups.

 

since cos2x+sin2x=1 we have

 

= (1)+(1)+(1)....8 times + cos245

 

now cos45=1/?2 putting the value we get

 

= 8 + 1/2 = 17/2 = RHS