Không dùng máy tính hãy tính:
A= \(Sin^25^o+Sin^225^o+Sin^245^o+Sin^265^o+Sin^285^o\)
B=\(tan1^o.tan2^o.tan3^o.......tan88^o.tan89^o\)
Không dùng mày tính hoặc bảng số, tính:
A =\(sin^25^o+sin^225^o+sin^245^o+sin^265^o+sin^285^o\).
Ta có: \(A=\sin^25^0+\sin^225^0+\sin^245^0+\sin^265^0+\sin^285^0\)
\(=\left(\sin^25^0+\sin^285^0\right)+\left(\sin^225^0+\sin^265^0\right)+\dfrac{1}{2}\)
\(=2+\dfrac{1}{2}=\dfrac{5}{2}\)
\(\Rightarrow A=\left(sin^25^0+sin^285^0\right)+\left(sin^225^0+sin^265^0\right)+sin^245^0=\left(sin^25^0+cos^25^0\right)+\left(sin^225^0+cos^225^0\right)+\dfrac{1}{2}=1+1+\dfrac{1}{2}=\dfrac{5}{2}\)
Bài 7: Tính
a/ \(A=2sin30^o-2cos60^o+tan45^0\)
b/ \(B=3sin^225^o+3sin^265^o-tan35^o+cotag55^o-\frac{cos32^o}{tan58^o}\)
c/ \(C=tan67^o-cotag23^o+cos^216^o+cos^274^o-\frac{4cotag37^o}{2tan53^o}\)
d/ \(D=2cotag37^ocotag53^o+sin^228^o-\frac{3tan54^o}{cotag36^o}+sin^262^o\)
e/ \(L=\left(sin1^o+sin2^o+....+sin88^o+sin89^o\right)-\left(cos1^o+cos2^o+cos3^o+....+cos88^o+cos89^o\right)\)
f/ \(M=tan1^o.tan2^o.tan3^o.....tan88^o.tan89^o\)
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 : \(E=cos^21+cos^22+cos^23+...+cos^289\)
\(=\left(cos^21+cos^289\right)+\left(cos^22+cos^288\right)+...+\left(cos^244+cos^246\right)+cos^245\)
\(=\left(cos^21+cos^2\left(90-1\right)\right)+\left(cos^22+cos^2\left(90-2\right)\right)+...+\left(cos^244+cos^2\left(90-44\right)\right)+cos^245\)
\(=\left(cos^21+sin^21\right)+\left(cos^22+sin^22\right)+...+\left(cos^244+sin^244\right)+cos^245\)\(=44+cos^245=44+\dfrac{1}{2}=\dfrac{89}{2}\)
Tính:
a)Tính A=\(sin^225^o\)+\(sin^265^o\)-tg\(35^o\)+cotg\(55^o\)-\(\dfrac{cotg32^o}{tg58^o}\)
b)Không dùng máy tính hãy tính cos\(30^o\)
b: \(\cos30^0=\dfrac{\sqrt{3}}{2}\)
Tinh:
\(A=cos^220^o+cos^230^o+...+cos^270^o.\)
\(B=sin^25^o+sin^225^o+sin^245^o+sin^265^o+sin^285^o.\)
jup mk vs
ap dung \(\sin a=\cos b\)
va ap dung\(sin^2a+cos^2a=1\)
bài 1 : không dùng bảng số hoặc máy tính, hãy tính :
a, A = \(\cos^220^o+\cos^230^o+\cos^240^o+.....+\cos^270^o\)
b, B = \(\sin^25^o+\sin^225^o+\sin^245^o+\sin^265^o+\sin^285^o\)
c, C = \(\sin^210^o-\sin^220^o+\sin^230^o-\sin^240^o-\sin^250^o-\sin^270^o+\sin^280^o\)
bài 2 : cho tam giác ABC vuông tại A, biết sin B = \(\frac{1}{4}\) C. Tính C ?
\(\sin^215+sin^225+sin^235+sin^255+sin^265+sin^275\)
\(sin^25+sin^225+sin^245+sin^265+sin^285\)
không dùng máy tính bỏ túi
sina=cos(90-a) thay vào ta được
sin215+sin225+sin235+cos235+cos225+cos215=3
tương tự câu dưới ta được =3/2
không dùng máy tính, tính \(\sin^235^o+\sin^265^o\)
`sin^2 25^o + sin^2 65^o`
`=cos^2 65^o + sin^2 65^o`
=1`
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`***` Áp dụng công thức lượng giác: `sin^2 \alpha +cos^2 \alpha =1`
Đề cs sai 0 nhỉ phải là `sin^2 25^o + sin^2 65^o`
Hoặc `sin^2 35^o + sin^2 55^o` chứ
tính nhanh
A=\(sin^242^o+sin^243^o+sin^244^o+sin^245^0+sin^246^o+sin^247^o+sin^248^o\)
B=\(\cos^215^o-cos^225^o+cos^235^o-cos^245^o+cos^255^o-cos^265^o+cos^275^o\)
\(ADCT:\sin^2\alpha+\cos^2\alpha=1\)
\(A=\left(\sin^242^0+\sin^248^0\right)+\left(\sin^243^0+\sin^247^0\right)+\left(\sin^244^0+\sin^246^0\right)+\sin45^0\)
\(A=\left(\sin^242^0+\cos^242^0\right)+\left(\sin^243^0+\cos^243^0\right)+\left(\sin^244^0+\cos^244^0\right)+\frac{\sqrt{2}}{2}\)
\(A=1+1+1+\frac{\sqrt{2}}{2}=\frac{6+\sqrt{2}}{2}\)
Câu b lm tương tự