Question

evaluate:sin²5+sin²10+......+sin²85+cos²45.​

Answer 1

Answer:

Step-by-step explanation:

sin^5+sin^10+.....+sin^40+sin^45+sin^50+.....sin^80+sin^85+cos^45

since cos^B+sin^B=1, and sinA=cos(90-A)

=sin^5+sin^10+.....+sin^40+cos^40+cos^35+...+cos^10+cos^5+1

=1×(40/5)+1

=9=Ans.

Answer 2

GIVEN:-

sin²5° + sin²10° + sin²15° + sin²20° + sin²25° + sin²30° + sin²35° + sin²40° + sin²45° + sin²50° + sin²55° + sin²60° + sin²65° + sin²70° + sin²75° + sin²80° + sin²85 + cos²45°

we know:-

sin²(90 - θ) = cos²θ

sin²θ + cos²θ = 1

now,

let us arrange the question in this form

then,

sin²(90 - 5) + sin²(90 - 80) + ......... + sin²85 + cos²85

=> cos²85 + cos²80 + cos²75 + cos²70 + cos²65 + cos²60 + cos²55 + cos²50 + sin²45 + sin²40+.........+sin²85 + cos²45

=> (cos²85 + sin²85) + (cos²80 + sin²80) + (cos²75 + sin²75) + (cos²70 + sin²70) + (cos²65 + sin²65) + (cos²60 + sin²60) + (cos²55 + sin²55) + (cos²50 + sin²50) + (cos²45 + sin²45)

=> 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1+ 1 = 9

hope it's helpful :-)