b) \(sin^23^o+sin^215^o+sin^275^o+sin^287^o\)

\(=\left(sin^23^o+cos^23^o\right)+\left(sin^215^o+cos^215^o\right)\)

\(=1+1=2\)

a) \(cos^212^o+cos^278^o+cos^21^o+cos^289^o\)

\(=\left(sin^278^o+cos^278^o\right)+\left(sin^289^o+cos^289^o\right)\)

\(=1+1=2\)

4. \(D=sin^21^o+sin^22^o+sin^23^o+...+sin^287^o+sin^288^o+sin^289^o=\left(sin^21^o+sin^289^o\right)+\left(sin^22^o+sin^288^o\right)+...+\left(sin^244^o+sin^246^o\right)+sin^245^o=1+1+1+...+1+1+0,5=44,5\)

\(5.E=cos^21^o+cos^22^o+cos^23^o+...+cos^287^o+cos^288^o+cos^289^o=\left(cos^21^o+cos^289^o\right)+\left(cos^22^o+cos^288^o\right)+...+\left(cos^244^o+cos^246^o\right)+cos^245^o=1+1+1+...+1+0,5=1.44+0,5=44,5\)

mk bỏ dấu độ hết nha bn : (trong toán người ta cho phép)

1) ta có : \(A=\left(sin1+sin2+...+sin89\right)-\left(cos1+cos2+...+cos89\right)\)

\(=\left(sin1+sin2+...+sin89\right)-\left(cos\left(90-89\right)+cos\left(90-88\right)+...+cos\left(90-1\right)\right)\)

\(=\left(sin1+sin2+...+sin89\right)-\left(sin89+sin88+...+sin1\right)=0\)

2) ta có : \(B=tan1.tan2.tan3...tan87.tan88.tan89\)

\(=\left(tan1.tan89\right).\left(tan2.tan88\right).\left(tan3.tan87\right)...\left(tan44.tan46\right).tan45\)

\(=\left(tan1.tan\left(90-1\right)\right).\left(tan2.tan\left(90-2\right)\right).\left(tan3.tan\left(90-3\right)\right)...\left(tan44.tan\left(90-44\right)\right).tan45\)

3) bạn xem lại đề nha

4) ta có : \(D=sin^21+sin^22+sin^23+...+sin^289\)

\(=\left(sin^21+sin^289\right)+\left(sin^22+sin^288\right)+...+\left(sin^244+sin^246\right)+sin^245\)

\(=\left(sin^21+sin^2\left(90-1\right)\right)+\left(sin^22+sin^2\left(90-2\right)\right)+...+\left(sin^244+sin^2\left(90-44\right)\right)+sin^245\)

\(=44+sin^245=44+\dfrac{1}{2}=\dfrac{89}{2}\)

5) ta có : \(E=cos^21+cos^22+cos^23+...+cos^289\)

\(=\left(cos^21+cos^289\right)+\left(cos^22+cos^288\right)+...+\left(cos^244+cos^246\right)+cos^245\)

\(=\left(cos^21+cos^2\left(90-1\right)\right)+\left(cos^22+cos^2\left(90-2\right)\right)+...+\left(cos^244+cos^2\left(90-44\right)\right)+cos^245\)

\(=44+cos^245=44+\dfrac{1}{2}=\dfrac{89}{2}\)

\(A=sin^21^o+c\text{os}^22^o+sin^23^o+c\text{os}^24^o+...+sin^2179^o+c\text{os}^2180^o\)

\(=sin^21^o+c\text{os}^22^o+sin^23^o+c\text{os}^24^o+...+c\text{os}^290^o-sin^289^o-c\text{os}^288^o-...-sin^21^o-c\text{os}^20^o\)

\(=c\text{os}^290^o-c\text{os}^20^o\)

\(=-1\)

Chúc bn học tốt

ai đó giúp giùm với ....help me

câu B sửa là B=tan1.tan2.tan3.............tan89

+ tan1 = cot89

... tan 89 = cot1

=> 2B = tan1.cot1.tan2.cot2...tan89.cot89

= 1.1...1 = 1

=> B = 1/2

Botay.com.vn

\(\cos^21^o+\cos^289^o=\cos^21^o+\cos^2\left(90^o-1^o\right)=\cos^21^o+\sin^21^o=1\)

\(\cos^22^o+\cos^288^o=\cos^22^o+\cos^2\left(90^o-2^o\right)=\cos^22^o+\sin^22^o=1\)

.......

\(\cos^244^o+\cos^246^o=\cos^244^o+\cos^2\left(90^o-44^o\right)=\cos^244^o+\sin^244^o=1\)

\(\cos^245^o=\left(\frac{\sqrt{2}}{2}\right)^2=\frac{1}{2}\)

=> \(A=1.44+\frac{1}{2}-\frac{1}{2}=44\)

Tự chứng minh từng cái này rồi suy ra cái đó nhé b.

Ta có: \(sin\frac{A}{2}cos\frac{B}{2}cos\frac{C}{2}-sin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}=sin^2\frac{A}{2}\)

Tương tự ta suy ra: 

\(sin\frac{A}{2}cos\frac{B}{2}cos\frac{C}{2}+cos\frac{A}{2}sin\frac{B}{2}cos\frac{C}{2}+cos\frac{A}{2}cos\frac{B}{2}sin\frac{C}{2}=sin^2\frac{A}{2}+sin^2\frac{B}{2}+sin^2\frac{C}{2}+3sin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}\left(1\right)\)

Tiếp theo chứng minh:

\(2sin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}=\frac{cosA+cosB+cosC-1}{2}\left(2\right)\)

\(sin^2\frac{A}{2}+sin^2\frac{B}{2}+sin^2\frac{C}{2}=\frac{3}{2}-\frac{cosA+cosB+cosC}{2}\left(3\right)\)

\(tan\frac{A}{2}tan\frac{B}{2}+tan\frac{B}{2}tan\frac{C}{2}+tan\frac{C}{2}tan\frac{A}{2}=1\left(4\right)\)

Từ (1), (2), (3), (4) suy được điều phải chứng minh

ko hiểu ( vì em mới học lớp 6)

trinh le na

cho bạn 4 năm nữa cũng chưa hiểu đâu