(Áp dụng tính chất lượng giác của hai góc phụ nhau.)

Vì 60o + 30o = 90o nên sin60o = cos30o

Vì 75o + 15o = 90o nên cos75o = sin15o

Vì 52o30' + 37o30' = 90o nên sin 52o30'= cos37o30'

Vì 82o + 8o = 90o nên cotg82o = tg8o

Vì 80o + 10o = 90o nên tg80o = cotg10o

Chọn B

Vd5:

a: \(cos42^0=\sin\left(90^0-42^0\right)=\sin48^0\)

\(cos67^0=\sin\left(90^0-67^0\right)=\sin23^0\)

Ta có: \(23^0<30^0<38^0<48^0<75^0\)

=>Sin23<sin30<sin38<sin48<sin 75

=>cos67<sin30<sin38<cos42<sin75

b: \(\cot49^0=\tan\left(90^0-49^0\right)=\tan41^0\)

\(\cot50^0=\tan\left(90^0-50^0\right)=\tan40^0\)

Ta có: 25<27<40<41<80

=>tan25<tan27<tan40<tan41<tan80

=>tan25<tan27<cot49<cot50<tan80

Vd6:

a: \(\sin^2a+cos^2a=1\)

=>\(cos^2a=1-0,8^2=1-0,64=0,36=0,6^2\)

=>cosa=0,6

tan a=sin a/cosa

=0,8/0,6

=4/3

cot a=cosa/sin a

=0,6/0,8=3/4

b: \(\sin^2a+cos^2a=1\)

=>\(\sin^2a=1-0,6^2=1-0,36=0,64\)

=>sin a=0,8

tan a=sin a/cosa

=0,8/0,6

=4/3

cot a=cosa/sin a

=0,6/0,8=3/4

c: \(\tan a\cdot\cot a=1\)

=>\(\cot a=\frac13\)

\(1+\tan^2a=\frac{1}{cos^2a}\)

=>\(\frac{1}{cos^2a}=1+3^2=1+9=10\)

=>\(cos^2a=\frac{1}{10}\)

=>\(cosa=\frac{1}{\sqrt{10}}=\frac{\sqrt{10}}{10}\)

Ta có: \(\sin^2a+cos^2a=1\)

=>\(\sin^2a=1-\frac{1}{10}=\frac{9}{10}\)

=>\(\sin a=\frac{3}{\sqrt{10}}\)

d: \(\tan a\cdot\cot a=1\)

=>\(\tan a=\frac12\)

Ta có: \(1+\tan^2a=\frac{1}{cos^2a}\)

=>\(\frac{1}{cos^2a}=1+\left(\frac12\right)^2=1+\frac14=\frac54\)

=>\(cos^2a=\frac45\)

=>\(cosa=\frac{2}{\sqrt5}\)

\(\sin^2a+cos^2a=1\)

=>\(\sin^2a=1-\frac45=\frac15\)

=>\(\sin a=\frac{1}{\sqrt5}\)

Vd5:

a: \(cos42^0=\sin\left(90^0-42^0\right)=\sin48^0\)

\(cos67^0=\sin\left(90^0-67^0\right)=\sin23^0\)

Ta có: 23<30<38<48<75

=>sin23<sin30<sin38<sin48<sin75

=>cos67<sin30<sin38<cos42<sin75

b: \(\cot49^0=\tan\left(90^0-49^0\right)=tan41^0\)

\(\cot50^0=\tan\left(90^0-50^0\right)=\tan40^0\)

Ta có: 25<27<40<41<80

=>tan 25<tan 27<tan 40<tan41<tan80

=>tan 25<tan27<cot49<cot50<tan80

Vd6:

a: \(\sin^2a+cos^2a=1\)

=>\(cos^2a=1-0,8^2=1-0,64=0,36=0,6^2\)

=>cosa=0,6

\(\tan a=\frac{\sin a}{cosa}=\frac{0.8}{0.6}=\frac43\)

\(\cot a=\frac{1}{\tan a}=1:\frac43=\frac34\)

b: \(\sin^2a+cos^2a=1\)

=>\(\sin^2a=1-0,6^2=1-0,36=0,64=0,8^2\)

=>sin a=0,8

\(\tan a=\frac{\sin a}{cosa}=\frac{0.8}{0.6}=\frac43\)

\(\cot a=\frac{1}{\tan a}=1:\frac43=\frac34\)

c: \(\tan a\cdot\cot a=1\)

=>\(\cot a=\frac13\)

Ta có: \(1+\tan^2a=\frac{1}{cos^2a}\)

=>\(\frac{1}{cos^2a}=1+3^2=10\)

=>\(cos^2a=\frac{1}{10}\)

=>\(cosa=\frac{1}{\sqrt{10}}\)

Ta có: \(\sin^2a+cos^2a=1\)

=>\(\sin^2a=1-\frac{1}{10}=\frac{9}{10}\)

=>\(\sin a=\frac{3}{\sqrt{10}}\)

d: \(\tan a\cdot\cot a=1\)

=>\(\tan a=\frac{1}{\cot a}=\frac12\)

Ta có: \(1+\tan^2a=\frac{1}{cos^2a}\)

=>\(\frac{1}{cos^2a}=1+\left(\frac12\right)^2=\frac54\)

=>\(cos^2a=\frac45\)

=>\(cosa=\frac{2}{\sqrt5}\)

Ta có: \(\sin^2a+cos^2a=1\)

=>\(sin^2a=1-\frac45=\frac15\)

=>sin a=\(\frac{1}{\sqrt5}\)

Vd5:

a: \(cos42^0=\sin\left(90^0-42^0\right)=\sin48^0\)

\(cos67^0=\sin\left(90^0-67^0\right)=\sin23^0\)

Ta có: 23<30<38<48<75

=>sin23<sin30<sin38<sin48<sin75

=>cos67<sin30<sin38<cos42<sin75

b: \(\cot49^0=\tan\left(90^0-49^0\right)=tan41^0\)

\(\cot50^0=\tan\left(90^0-50^0\right)=\tan40^0\)

Ta có: 25<27<40<41<80

=>tan 25<tan 27<tan 40<tan41<tan80

=>tan 25<tan27<cot49<cot50<tan80

Vd6:

a: \(\sin^2a+cos^2a=1\)

=>\(cos^2a=1-0,8^2=1-0,64=0,36=0,6^2\)

=>cosa=0,6

\(\tan a=\frac{\sin a}{cosa}=\frac{0.8}{0.6}=\frac43\)

\(\cot a=\frac{1}{\tan a}=1:\frac43=\frac34\)

b: \(\sin^2a+cos^2a=1\)

=>\(\sin^2a=1-0,6^2=1-0,36=0,64=0,8^2\)

=>sin a=0,8

\(\tan a=\frac{\sin a}{cosa}=\frac{0.8}{0.6}=\frac43\)

\(\cot a=\frac{1}{\tan a}=1:\frac43=\frac34\)

c: \(\tan a\cdot\cot a=1\)

=>\(\cot a=\frac13\)

Ta có: \(1+\tan^2a=\frac{1}{cos^2a}\)

=>\(\frac{1}{cos^2a}=1+3^2=10\)

=>\(cos^2a=\frac{1}{10}\)

=>\(cosa=\frac{1}{\sqrt{10}}\)

Ta có: \(\sin^2a+cos^2a=1\)

=>\(\sin^2a=1-\frac{1}{10}=\frac{9}{10}\)

=>\(\sin a=\frac{3}{\sqrt{10}}\)

d: \(\tan a\cdot\cot a=1\)

=>\(\tan a=\frac{1}{\cot a}=\frac12\)

Ta có: \(1+\tan^2a=\frac{1}{cos^2a}\)

=>\(\frac{1}{cos^2a}=1+\left(\frac12\right)^2=\frac54\)

=>\(cos^2a=\frac45\)

=>\(cosa=\frac{2}{\sqrt5}\)

Ta có: \(\sin^2a+cos^2a=1\)

=>\(sin^2a=1-\frac45=\frac15\)

=>sin a=\(\frac{1}{\sqrt5}\)

vd5 :cos67^o,sin30^o,sin38^o,cos42^o ,sin75^o

        tan25^o,  tan27^o, cot50^o,cot49^o,tan80^o