Tính:
a) \(\cos^212+\cos^278+\cos^21+\cos^289\)
b) \(\sin^23+\sin^215+\sin^275+\sin^287\)
c) \(\sin^21+\sin^22+\sin^33+...+\sin^288+\sin^289\)
A=\(\cos^21+\cos^22+\cos^23+.......+\cos^287+\cos^288+\cos^289-\frac{1}{2}\)
B=\(\sin^21+\sin^22+\sin^23+....+\sin^287+\sin^288+\sin^289-\frac{1}{2}\)
C=\(\tan^21\times\tan^22\times\tan^23\times.....\times\tan^287\times\tan^288+\tan^289\)
D=\(\left(\tan^21\div\cot^289\right)+\left(\tan^22\div\cot^288\right)+......+\left(\tan^244\div\cot^246\right)+\tan^245\)
các bạn giúp mình với
tất cả các số đều có độ hết nha trừ cái 1/2 là không có dộ
\(A=cos^21+coss^22+...+cos^288+cos^289-\frac{1}{2}\)
\(A=1-sin^21+1-sin^22+...+1-sin^244+cos^245+cos^246+...+cos^289-\frac{1}{2}\)
\(A=1\cdot44+cos^245-\frac{1}{2}\)
\(A=44\)
B=\(sin^21+sin^22+...+sin^289-\frac{1}{2}\)
\(B=1-cos^21+1-cos^22+...+sin^245+sin^246+....+sin^289-\frac{1}{2}\)
\(B=1\cdot44+sin^245-\frac{1}{2}=44\)
\(C=tan^21\cdot tan^22\cdot...\cdot tan^288+tan^289\)
\(C=tan^21\cdot\left(tan^22\cdot tan^288\right)\cdot...\cdot\left(tan^244\cdot tan^246\right)\cdot tan^245+tan^289\)
\(C=tan^21+tan^289\approx3282\)
D = \(\left(tan^21:cot^289\right)+...+\left(tan^244:tan^246\right)+tan^245\)
\(D=\left(tan^21\cdot tan^289\right)+...+\left(tan^244\cdot tan^246\right)+tan^245\)
\(D=1+...+1+1\)
ta thấy từ 1 đến 89 có 89 số hạng, trong đó có 44 cặp.
vậy D = 45
Tính :
a) A=\(\sin^210'+\sin^220'+...+\sin^270'+\sin^280'\)
b) B=\(\cos^212'+\cos^278'+\cos^21'+\cos^289'\)
Note : ' là độ nha!
áp dụng sin2a=cos2(90-a)
và sin2a+cos2a=1
s2 Lắc Lư s2 ko sai! but chưa detail bn nhé!
Tinhs giá trị biểu thức
a, A= \(\frac{sin33}{cos57}\)+\(\frac{tan32}{cotg58}\)- 2 \(\left(sin20cos70+cos20sin70\right)\)
b,B=\(\frac{sin^215+sin^275-sin^212-sin^278}{cos^213+cos^277+cos^21+cos^289}\)+ \(\frac{2tan55}{cotg35}\)
\(A=\frac{\cos57}{\cos57}+\frac{\cot58}{\cot58}-2\left(1+1\right)\)\()\)
=1+1-4
=-2
Tính giá trị các biểu thức sau:
1. A=\(\left(sin1^o+sin2^o+sin3^o+...+sin88^o+sin89^o\right)-\left(cos1^o+cos2^o+cos3^o+...+cos88^o+cos89^o\right)\)
2. B= \(\left(tan1^o.tan2^o.tan3^o...tan87^o.tan88^o.tan89^o\right)\)
3. C=\(cot1^o.cot2^o.cot3^o...tan87^o.tan88^o.tan89^o\)
4. D= \(sin^21^o+sin^22^o+sin^23^o+...+sin^287^o+sin^288^o+sin^289^o\)
5. E = \(cos^21^o+cos^22^o+cos^23^o+...+cos^287^o+cos^288^o+cos^289^o\)
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 : \(B=tan1.tan2.tan3...tan87.tan88.tan89\)
\(=\left(tan1.tan89\right).\left(tan2.tan88\right).\left(tan3.tan87\right)...\left(tan44.tan46\right).tan45\)
\(=\left(tan1.tan\left(90-1\right)\right).\left(tan2.tan\left(90-2\right)\right).\left(tan3.tan\left(90-3\right)\right)...\left(tan44.tan\left(90-44\right)\right).tan45\)
\(=\left(tan1.cot1\right).\left(tan2.cot2\right).\left(tan3.cot3\right)...\left(tan44.cot44\right).tan45\) \(=tan45=1\)3) bạn xem lại đề nha
4) ta có : \(D=sin^21+sin^22+sin^23+...+sin^289\)
\(=\left(sin^21+sin^289\right)+\left(sin^22+sin^288\right)+...+\left(sin^244+sin^246\right)+sin^245\)
\(=\left(sin^21+sin^2\left(90-1\right)\right)+\left(sin^22+sin^2\left(90-2\right)\right)+...+\left(sin^244+sin^2\left(90-44\right)\right)+sin^245\)
\(=\left(sin^21+cos^21\right)+\left(sin^22+cos^22\right)+...+\left(sin^244+cos^244\right)+sin^245\)\(=44+sin^245=44+\dfrac{1}{2}=\dfrac{89}{2}\)
5) ta có : \(E=cos^21+cos^22+cos^23+...+cos^289\)
\(=\left(cos^21+cos^289\right)+\left(cos^22+cos^288\right)+...+\left(cos^244+cos^246\right)+cos^245\)
\(=\left(cos^21+cos^2\left(90-1\right)\right)+\left(cos^22+cos^2\left(90-2\right)\right)+...+\left(cos^244+cos^2\left(90-44\right)\right)+cos^245\)
\(=\left(cos^21+sin^21\right)+\left(cos^22+sin^22\right)+...+\left(cos^244+sin^244\right)+cos^245\)\(=44+cos^245=44+\dfrac{1}{2}=\dfrac{89}{2}\)
Khong dùng máy tính cầm tay, hãy tính:
a) A = \(\dfrac{\sin33}{\cos57}+\dfrac{\tan32}{\cot58}-2\left(\sin20\cdot\cos70+\cos20\cdot\sin70\right)\)
b) B = \(\dfrac{\sin^215+\sin^275-\sin^212-\sin^218}{\cos^213+\cos^277+\cos^21+\cos^289}+\dfrac{2\cdot\tan55}{\cot35}\)
a) ta có : \(A=\dfrac{sin33}{cos57}+\dfrac{tan32}{cot58}-2\left(sin20.cos70+cos20.sin70\right)\)
\(\Leftrightarrow A=\dfrac{sin33}{cos\left(90-33\right)}+\dfrac{tan32}{cot\left(90-32\right)}-2\left(sin20.cos\left(90-20\right)+cos20.sin\left(90-20\right)\right)\)
\(\Leftrightarrow A=\dfrac{sin33}{sin33}+\dfrac{tan32}{tan32}-2\left(sin20.sin20+cos20.cos20\right)\)\(\Leftrightarrow A=1+1-2\left(sin^220+cos^220\right)=1+1-2=0\)
b) sữa đề chút nha
ta có : \(B=\dfrac{sin^215+sin^275-sin^212-sin^278}{cos^213+cos^277+cos^21+cos^289}+\dfrac{2tan55}{cot35}\)
\(\Leftrightarrow B=\dfrac{sin^215+sin^2\left(90-15\right)-sin^212-sin^2\left(90-12\right)}{cos^213+cos^2\left(90-13\right)+cos^21+cos^2\left(90-1\right)}+\dfrac{2tan\left(90-35\right)}{cot35}\)
\(\Leftrightarrow B=\dfrac{sin^215+cos^215-sin^212-cos^212}{cos^213+sin^213+cos^21+sin^21}+\dfrac{2cot35}{cot35}\) \(\Leftrightarrow B=\dfrac{sin^215+cos^215-\left(sin^212+cos^212\right)}{cos^213+sin^213+cos^21+sin^21}+\dfrac{2cot35}{cot35}\)\(\Leftrightarrow B=\dfrac{1-1}{cos^213+sin^213+cos^21+sin^21}+2=0+2=2\)
tính giá trị các biểu thức sau
A = \(\sin^210^o+\sin^220^o+...+\sin^270^o+\sin^280^o\)
B = \(\cos^212^o+\cos^278^o+\cos^21^o+\cos^289^o\)
Bạn nào biết giúp mình nha mình đang cần gấp cảm ơn
B=\(\tan1.tan2.tan3.tan89\)
\(C=\sin^254+sin^236-3sin^2126+.......+\cos^3126+\cos^354-3\cos^254\)
\(D=sin^21+sin^22+sin^23+......+sin^289+sin^290\)
p/s: mí bạn giúp đỡ giùm....tớ mới học dạng này lên còn hơi bỡ ngỡ ....đang cần gấp lắm ag!!
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
B1... Cho \(\Delta ABC\) nhọn AB=c , AC= b , CB=a
CMR : \(\dfrac{a}{\sin a}=\dfrac{b}{\sin b}=\dfrac{c}{\sin c}\)
B2... Không dùng bảng số và m.tính . Hãy tính
a) \(\sin^212^o+\sin^222^o+\sin^232^o+\sin^258^o+\sin^268^o+\sin^278^o\)
b)\(\cos^215^o+\cos^225^o+\cos^235^o+\cos^255^o+\cos^265^o+\cos^275^o-3\)
c) \(4\cos^2\alpha-6\sin^2\alpha,\) biết \(\sin\alpha=\dfrac{1}{5}\)
d) \(\sin\alpha.\cos\alpha\) biết \(\tan\alpha+\cot\alpha=3\)
a) Ta có : sin\(^2\)12o=cos278o=> sin212o+sin278o=1.
tương tự => A=3
b) tương tự câu (a) ta có: cos215o=sin275o ( do 15+75=90 nha bạn ) => cos215o+cos275o=1. Tương tự => B=0
c) Ta có: C= 4cos2a -6sin2a=4(cos2a+sin2a)-10sin2a=4-10.\(\dfrac{1}{5^2}\)=4-0,4=3,6
\(A=sin^21^o+cos^22^o+sin^23^o+cos^24^o+...+sin^2179^o+cos^2180^o\)
\(A=sin^21^o+c\text{os}^22^o+sin^23^o+c\text{os}^24^o+...+sin^2179^o+c\text{os}^2180^o\)
\(=sin^21^o+c\text{os}^22^o+sin^23^o+c\text{os}^24^o+...+c\text{os}^290^o-sin^289^o-c\text{os}^288^o-...-sin^21^o-c\text{os}^20^o\)
\(=c\text{os}^290^o-c\text{os}^20^o\)
\(=-1\)
Chúc bn học tốt