cos square 5 + cos square 10 + cos square 15 + 1 + cos square 90 is equals to
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The correct question is To find the value of cos²5 + cos²10 + ..... + cos²85 + cos²90.
ANSWER:
The value of cos²5+cos²10+ .....+cos²85+cos²90 is 17/2.
- We know that sin(90-θ) = cosθ.
- We have to find the value of cos²5+cos²10+cos²15+cos²20+...+cos²90
- Total number of terms = 18
- Now, we substitute cosθ = sin(90-θ).
- cos²5 + cos²10 + cos²15 + .... + cos²40 + cos²45 + sin²(90-50) + sin²(90-55) +....+ sin²(90-80)+ sin²(90-85)+ cos²90
= (cos²5+sin²5) + (cos²10+sin²10) + (cos²15+sin²15)+ .... (cos²40+sin²40) + cos²45+cos²90
= 8+1/2+0= 17/2
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