Answer:
11. D. All of these
12.
sin30° =[tex]\frac{1}{2}[/tex]
cos 45°=[tex]\frac{1}{\sqrt{2} }[/tex]
cos 30°=[tex]\frac{\sqrt{3} }{2}[/tex]
tan 45°=[tex]1[/tex]
tan 30°=[tex]\frac{1}{\sqrt{3} }[/tex]
13. B tan 60°
Step-by-step explanation:
11.Given,
ABC is a triangle with sides measures as [tex]AB=c , AC=b \ and\ BC=a[/tex]
We have to find the different trigonometric ratio,
We know,
[tex]sin=\frac{opposite}{hypotenuse} \ and\ cos=\frac{adjacent}{hypotenuse}[/tex]
We observe,
[tex]sinA=\frac{a}{c} \\cosB=\frac{a}{c}[/tex]
Therefore both are equal, option (A) is correct!
It is a rule that,
[tex]sin(90-M) = cosM[/tex]
Thus option (B) is correct!
It is a universal proof that ,
[tex]sin^2M+cos^2M=1[/tex]
Thus option (C) is true!
Therefore option (D) is the appropriate choice 'all of these' are correct!
12.
We know,
[tex]sin=\frac{opp}{hyp} \\sin30=\frac{1}{2}[/tex]
We know ,
[tex]cos=\frac{adj}{hyp} \\cos45=\frac{1}{\sqrt{2} }[/tex]
Similarly,
[tex]co30=\frac{\sqrt{3} }{2}[/tex]
We know,
[tex]tan=\frac{opp}{hyp} \\tan=\frac{1}{1} =1[/tex]
Similarly,
[tex]tan30=\frac{1}{\sqrt{3} }[/tex]
13.
We know,
[tex]\frac{sin60}{cos60} =\sqrt{3} \\tan60=\sqrt{3}[/tex]
Therefore B is the correct option!
