Answer:
1. [tex]\tan \theta[/tex] is not defined at [tex]\theta = \frac{\pi}{2}[/tex]
2. none of the option holds true
3. Option A
Step-by-step explanation:
1.
[tex]\tan \theta = \frac{\sin \theta}{\cos\theta}[/tex]
[tex]\tan \frac{\pi}{2} = \frac{\sin \frac{\pi}{2}}{\cos \frac{\pi}{2}}[/tex]
[tex]\sin \frac{\pi}{2} = 1[/tex]
[tex]\cos \frac{\pi}{2} =0[/tex]
[tex]\tan \frac{\pi}{2} = \frac{1}{0}[/tex]
Hence
[tex]\tan \frac{\pi}{2}[/tex] is not defined
2.
[tex]\frac{x}{12} = \sin 20[/tex]
[tex]\frac{x}{12} = \cos 70[/tex]
[tex]\frac{12}{x} = \cosec 20[/tex]
[tex]\frac{12}{x} = \sec 70[/tex]
None of the above is given in the options
3.
The rule says
[tex]\tan (-\theta)= - \tan \theta[/tex]
[tex]\tan(-\frac{\pi}{3})= - \tan \frac{\pi}{3}[/tex]
[tex]\tan(-\frac{\pi}{3})= - \sqrt 3[/tex]
Hence option A is correct
