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1.\(\sin^2\alpha+\cos^2\alpha=1\)
\(\Rightarrow\cos^2\alpha=1-\sin^2\alpha=1-\left(\frac{3}{5}\right)^2=1-\frac{9}{25}=\frac{16}{25}\)
\(\Rightarrow\cos\alpha=\frac{4}{5}\)
\(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{4}\)
\(\cot\alpha=\frac{\cos\alpha}{\sin\alpha}=\frac{\frac{4}{5}}{\frac{3}{5}}=\frac{4}{3}\)
2.\(\sin^2\alpha+\cos^2\alpha=1\)
\(\Rightarrow\sin^2\alpha=1-\cos^2\alpha=1-\left(0,8\right)^2=1-0,64=0,36\)
\(\Rightarrow\sin\alpha=0,6\)
\(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}=\frac{0,6}{0,8}=\frac{3}{4}\)
\(\tan\alpha.\cot\alpha=1\Rightarrow\cot\alpha=\frac{1}{\tan\alpha}=\frac{1}{\frac{3}{4}}=\frac{4}{3}\)
tuỳ ý giá trị biểu thức
a/ Có vế trái = \(\left(sin^2\alpha+cos^2\alpha\right)^2=1^2=1\) (= vế phải)
b/ Vế trái = \(tan^2\alpha.\left(1-sin^2\alpha\right)=tan^2\alpha.cos^2\alpha=sin^2\alpha\)(= vế phải)
c/ Vế trái = \(cos^2\alpha.\left(1+tan^2\alpha\right)=cos^2\alpha.\frac{1}{cos^2\alpha}=1\) (= vế phải)
a) ta có : \(A=tan1.tan2.tan3...tan89\)
\(=\left(tan1.tan89\right).\left(tan2.tan88\right).\left(tan3.tan87\right)...\left(tan44.tan46\right).tan45\)
\(=\left(tan1.tan\left(90-1\right)\right).\left(tan2.tan\left(90-2\right)\right).\left(tan3.tan\left(90-3\right)\right)...\left(tan44.tan\left(90-44\right)\right).tan45\)
\(=\left(tan1.cot1\right).\left(tan2.cot2\right).\left(tan3.cot3\right)...\left(tan44.cot44\right).tan45\) \(=tan45=1\)b) ta có \(B=\dfrac{sin\alpha+2cos\alpha}{3sin\alpha-4cos\alpha}=\dfrac{\dfrac{sin\alpha}{cos\alpha}+\dfrac{2cos\alpha}{cos\alpha}}{\dfrac{3sin\alpha}{cos\alpha}-\dfrac{4cos\alpha}{cos\alpha}}\)
\(=\dfrac{tan\alpha+2}{3tan\alpha-4}=\dfrac{\dfrac{1}{2}+2}{\dfrac{3}{2}-4}=-1\)
ta có \(D=\dfrac{2sin^2\alpha-3cos^2\alpha}{4cos^2\alpha-5sin^2\alpha}=\dfrac{\dfrac{2sin^2\alpha}{cos^2\alpha}-\dfrac{3cos^2\alpha}{cos^2\alpha}}{\dfrac{4cos^2\alpha}{cos^2\alpha}-\dfrac{5sin^2\alpha}{cos^2\alpha}}\)
\(=\dfrac{2tan^2\alpha-3}{4-5tan^2\alpha}=\dfrac{2\left(\dfrac{1}{2}\right)^2-3}{4-5\left(\dfrac{1}{2}\right)^2}=\dfrac{-10}{11}\)
\(\frac{\cos a-\sin a}{cosa+sina}=\frac{\frac{cosa}{cosa}-\frac{sina}{cosa}}{\frac{cosa}{cosa}+\frac{sina}{cosa}}\)(chia ca tu va mau cho cosa)
\(=\frac{1-tana}{1+tana}=vt\left(dpcm\right)\)
\(\Delta\)ABC vg tại A , ad tỉ số lg giác trong tg vg ta có
a,\(\sin^2\alpha+\cos^2\alpha\)=\(\frac{AB^2}{BC^2}\)+ \(\frac{AC^2}{BC^2}\)= \(\frac{BC^2}{BC^2}\)=1
b,\(\frac{\sin\alpha}{\cos\alpha}\)= \(\frac{AB}{BC}\): \(\frac{AC}{BC}\)= \(\frac{AB}{AC}\)= \(\tan\alpha\)
#mã mã#
a: \(1+cot^2\alpha=\dfrac{1}{sin^2\alpha}\)
=>\(cot^2\alpha=1:\dfrac{1}{9}-1=9-1=8\)
=>\(cot\alpha=2\sqrt{2}\)
=>\(tan\alpha=\dfrac{1}{2\sqrt{2}}=\dfrac{\sqrt{2}}{4}\)
b: \(1+tan^2\alpha=\dfrac{1}{cos^2\alpha}\)
=>\(1+tan^2\alpha=1:\left(\dfrac{2}{\sqrt{5}}\right)^2=\dfrac{5}{4}\)
=>\(tan^2\alpha=\dfrac{1}{4}\)
=>\(tan\alpha=\dfrac{1}{2}\)