Question

Cos²10+Cos²20+Cos²30+Cos²40+Cos²50+Cos²60+Cos²70+Cos²80+Cos²90.

Answer 1

Answer:

$\bf\;cos^210+cos^220+cos^230+cos^240+cos^250+cos^260+cos^270+cos^280+cos^290=4$

Step-by-step explanation:

$cos^210+cos^220+cos^230+cos^240+cos^250+cos^260+cos^270+cos^280+cos²90$

Using

$\boxed{\bf\;cos\,\theta=sin(90-\theta)}$

$\implies\boxed{\begin{minipage}{3cm} cos\,80=sin\,10\\\\cos\,70=sin\,20\\\\cos\,60=sin\,30\\\\cos\,50=sin\,40 \end{minipage}}$

$=cos^210+cos^220+cos^230+cos^240+sin^240+sin^230+sin^220+sin^210+0$

$=(cos^210+sin^210)+(cos^220+sin^220)+(cos^230+sin^230)+(cos^240+sin^240)$

Using

$\boxed{\bf\;cos^2\theta+sin^2\theta=1}$

$=1+1+1+1$

$=4$

Answer 2

= (cos²10+cos²80) + (cos²20+cos²70) + (cos²30+cos²60) + (cos²40+cos²50) + cos²90

= (cos²10+sin²10) + (cos²20+sin²20) + (cos²30+sin²30) + (cos²40+sin²40) + 0²

= 1 + 1 + 1 + 1

= 4

Mark as brainliest please