The value of cos square 1 + cos squared 2 + cos square 3 and so on up to cos square 90
Answers
Cos²1° + Cos²2° + Cos²3°+.................................+ Cos²89° + Cos²90° = 44.5
Step-by-step explanation:
Cos²1° + Cos²2° + Cos²3° +.......................................+ Cos²89° + Cos²90°
= Cos²1° + Cos²2° + Cos²3° + .......+ Cos²44° + Cos²45° + Cos²46° +.............+ Cos²89° + Cos²90°
now using Cosα = Sin(90 - α)
Cos²46° = Sin²44°
Cos²89° = Sin²1°
Cos²88° = Sin²2°
= Cos²1° + Cos²2° + Cos²3° + .......+ Cos²44° + Cos²45° +Sin²44° +.............+ Sin²1° + Sin²0°
Sin0° = 0
= Cos²1° + Cos²2° + Cos²3° + .......+ Cos²44° + Cos²45° +Sin²46° +.............+ Sin²1°
= (Cos²1° + Sin²1° ) + (Cos²2° + Sin²2° ) +..............................+ (Cos²44° + Sin²44° ) + Cos²45°
Cos²α + Sin²α = 1
= 1 + 1 + + 44(times) + Cos²45°
Cos²45° = 1/2
= 44 + 1/2
= 44.5
Cos²1° + Cos²2° + Cos²3° +.............................+ Cos²89° + Cos²90° = 44.5
Learn more:
1/cos0.cos1 + 1/cos1.cos2 +1/cos2.cos3 +.....+1/cos88.cos89
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sin theta/1-cos theta + tan theta / 1+cos theta = sec theta.cosec theta ...
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Answer:
44.5
Step-by-step explanation:
