Question :  If $\sec\theta +\tan\theta = 3$, then what is the value of $\sec \theta-\tan \theta$?

Option 1: $\frac{1}{3}$

Option 2: $6$

Option 3: $\frac{1}{6}$

Option 4: $\frac{1}{5}$

Question : If $\sec \theta+\tan \theta=4$, then $\sec \theta-\tan \theta=$___________.

Option 1: $\frac{1}{4}$

Option 2: $\frac{1}{2}$

Option 3: 2

Option 4: 4

Question : If $\sqrt{2} \sec ^2 \theta-4 \sec \theta+2 \sqrt{2}=0$, then what is the value $\sin ^2 \theta+\tan ^2 \theta$?

Option 1: $\frac{1}{2}$

Option 2: $\frac{2}{3}$

Option 3: $\frac{5}{2}$

Option 4: $\frac{3}{2}$

Question : If $\sec\theta+\tan\theta=a$, then what is the value of $\sec\theta$?

Option 1: $\frac{a+1}{2a^2}$

Option 2: $\frac{(a-1)}{2a^2}$

Option 3: $\frac{a^2-1}{2a}$

Option 4: $\frac{a^2+1}{2a}$

Question : If $\sqrt{3} \tan ^2 \theta-4 \tan \theta+\sqrt{3}=0$, then what is the value of $\tan ^2 \theta+\cot ^2 \theta$?

Option 1: $\frac{4}{3}$

Option 2: $\frac{10}{3}$

Option 3: $3$

Option 4: $\frac{6}{5}$