Rút gọn
\(1,D=cos^220^0+cos^230^0+cos^240^0+cos^250^0+cos^260^0+cos^270^0\)
\(2,E=sin^25^0+sin^225^0+sin^245^0+sin^265^0+sin^285^0\)
\(3,F=sin^6\alpha+cos^6\alpha+3sin^2\alpha.cos^2\alpha\)
Rút gọn
\(1,D=cos^220^0+cos^230^0+cos^240^0+cos^250^0+cos^260^0+cos^270^0\)
\(2,E=sin^25^0+sin^225^0+sin^245^0+sin^265^0+sin^285^0\)
\(3,F=sin^6\alpha+cos^6\alpha+3sin^2\alpha.cos^2\alpha\)
Bài 1 :
\(D=cos^220^0+cos^230^0+cos^240^0+cos^250^0+cos^260^0+cos^270^0\)
\(=\left(cos^220^0+cos^270^0\right)+\left(cos^230^0+cos^260^0\right)+\left(cos^240^0+cos^250^0\right)\)
\(=1+1+1=3\)
Bài 2 :
\(E=sin^25^0+sin^225^0+sin^245^0+sin^265^0+sin^285^0\)
\(=\left(sin^25^0+sin^285^0\right)+\left(sin^225^0+sin^265^0\right)+sin^245^0\)
\(=1+1+\dfrac{1}{2}=\dfrac{5}{2}\)
Bài 3 :
\(F=sin^6\alpha+cos^6\alpha+3sin^2\alpha.cos^2\alpha\)
\(=1-3sin^2\alpha.cos^2\alpha+3sin^2a.cos^2\alpha\)
\(=1\)
Đáp án:
Giải thích các bước giải:
1.D = cos²20 + cos²30 +cos²40 + cos²50 +cos²60 +cos²70
D = sin²70 + cos²70 + sin²60 +cos²60 + sin²50 +cos²50
D = 1 + 1 + 1 = 3
2.E = sin²5 + sin²25 + sin²45 + sin² 65 +sin²85
E = cos²85 +cos²65 +sin²45 +sin² 65 +sin²85
E = 1 + 1 + (√2/2)² = 5/2
3. F = sin^6∝ +cos^6∝ + 3sin²∝.cos∝²
= (sin²∝ +cos²∝)(sin^4∝ -sin²∝.cos∝² + cos^4∝) + 3sin²∝.cos∝²
= (sin²∝ +cos²∝)² -3sin²∝.cos∝² + 3sin²∝.cos∝²
= 1