\(\frac{3cos77.3cotan77}{2tan13}\)-\(\frac{cos^226+cos^{64^{ }}-cos^271-cos^215}{sin^234+sin^{56}+sin^{2^{ }}15+sin^275}\)
Tính giá trị của biểu thức:
\(A=\frac{3\cos67^0}{2\tan23^0}-\frac{\cos^236^0+\cos^254^0-\cos^217^0-\cos^273^0}{\sin^224^0+\sin^266^0+\sin^215^0+\sin^275^0}\)
tính
a)A= \(sin^2\frac{\pi}{3}+sin^2\frac{\pi}{9}+sin^2\frac{7\pi}{18}+sin^2\frac{\pi}{6}\)
b) B= \(sin^2\frac{\pi}{6}+sin^2\frac{\pi}{3}+sin^2\frac{\pi}{4}+sin^2\frac{9\pi}{4}+tan\frac{\pi}{6}.cot\frac{\pi}{6}\)
c) C= \(cos^215+cos^225+cos^235+cos^245+cos^2105+cos^2115+cos^2125\)
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 của các biểu thức sau:
a) \(A = \frac{{\sin \frac{\pi }{{15}}\cos \frac{\pi }{{10}} + \sin \frac{\pi }{{10}}\cos \frac{\pi }{{15}}}}{{\cos \frac{{2\pi }}{{15}}\cos \frac{\pi }{5} - \sin \frac{{2\pi }}{{15}}\sin \frac{\pi }{5}}}\); b) \(B = \sin \frac{\pi }{{32}}\cos \frac{\pi }{{32}}\cos \frac{\pi }{{16}}\cos \frac{\pi }{8}\).
a) \(A = \frac{{\sin \frac{\pi }{{15}}\cos \frac{\pi }{{10}} + \sin \frac{\pi }{{10}}\cos \frac{\pi }{{15}}}}{{\cos \frac{{2\pi }}{{15}}\cos \frac{\pi }{5} - \sin \frac{{2\pi }}{{15}}\sin \frac{\pi }{5}}} = \frac{{\sin \left( {\frac{\pi }{{15}} + \frac{\pi }{{10}}} \right)}}{{\cos \left( {\frac{{2\pi }}{{15}} + \frac{\pi }{5}} \right)}} = \frac{{\sin \frac{\pi }{6}}}{{\cos \frac{\pi }{3}}} = 1\)
b) \(B = \sin \frac{\pi }{{32}}\cos \frac{\pi }{{32}}\cos \frac{\pi }{{16}}\cos \frac{\pi }{8} = \frac{1}{2}\sin \frac{\pi }{{16}}.\cos \frac{\pi }{{16}}.\cos \frac{\pi }{8} = \frac{1}{4}\sin \frac{\pi }{8}.\cos \frac{\pi }{8} = \frac{1}{8}\sin \frac{\pi }{4} = \frac{1}{8}.\frac{{\sqrt 2 }}{2} = \frac{{\sqrt 2 }}{{16}}\;.\)
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
Giúp em với , em kém lượng giác lắm ;; ;;
Tính giá trị biểu thức
a) A= \(sin^2\frac{\pi}{3}+sin^2\frac{\pi}{9}+sin^2\frac{7\pi}{18}+sin^2\frac{\pi}{6}\)
b) B= \(sin^2\frac{\pi}{6}+sin^2\frac{\pi}{3}+sin^2\frac{\pi}{4}+sin^2\frac{9\pi}{4}+tan\frac{\pi}{6}.cot\frac{\pi}{6}\)
c) C= \(cos^215+cos^225+cos^235+cos^245+cos^2105+cos^2115+cos^2125\)
Tính:
a) \(\cos^212+\cos^278+\cos^21+\cos^289\)
b) \(\sin^23+\sin^215+\sin^275+\sin^287\)
c) \(\sin^21+\sin^22+\sin^33+...+\sin^288+\sin^289\)
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) \(cos^212^o+cos^278^o+cos^21^o+cos^289^o\)
\(=\left(sin^278^o+cos^278^o\right)+\left(sin^289^o+cos^289^o\right)\)
\(=1+1=2\)
Tính giá trị của biểu thức:
a,A= \(sin^215^0+sin^240^0+sin^260^0+sin^275^0+sin^250^0+sin^230^0\)
b, B=\(tan5^0tan10^0....tan85^0\)
c, C=\(cos^215^0-cos^225^0+cos^235^0-cos^245^0-cos^265^0+cos^275^0\)
LÀM ƠN GIÚP MÌNH NHÉ, MAI NỘP RÙI. PLEASE!!!!!!
Có
A=\(\left(sin^215^o+sin^275^o\right)+\left(sin^240^o+sin^250^o\right)+\left(sin^260^o+sin^230^o\right)\)
\(=\left(sin^215^o+cos^215^o\right)+...\)
\(=1\cdot3=3\)
Câu c tương tự mà mk nghĩ đề sai dấu - trước cos^245độ
Nói chung nếu: a+b=90 độ
thì: \(sin^2a+sin^2b=1\)
b) thì áp dụng nếu a+b=90 độ:
\(tana=cotb\) và ngược lại
Mà \(tana\cdot cota=1\)
Nói chung là công thức......
\(\sin^275^o+\sin^215^o-\cos^250^o-\cos^240^o+\cot45^o.\cot45^o\)
áp dụng \(sin^2a+\cos^2a=1\)
ta có \(\sin^275^o+sin^215^o-\cos^250^o-\cos^240^o+\)\(cot45^o.cot45^o\)\(=sin^275^o+\cos^275^o-\left(\cos^250^o+sin^250^o\right)\)\(+cot^245^o\)\(=1-1+1=1\)
vì đây là tam giác vuông, hai góc nhọn phụ nhau nên sin góc này bằng cosin góc kia