Question : If $0°<A<90°$, the value of $\frac{\tan A\ -\ \sec A\ -\ 1}{\tan A\ +\ \sec A\ +\ 1}$ is:

Option 1: $\frac{\sin A-1}{\cos A}$

Option 2: $\frac{1-\sin A}{\cos A}$

Option 3: $\frac{1-\cos A}{\sin A}$

Option 4: $\frac{\sin A+1}{\cos A}$

Question : If $\frac{\cos\alpha}{\cos\beta}= m$ and $\frac{\cos\alpha}{\sin\beta}= n$, then the value of $(m^{2}+n^{2})\cos^{2}\beta$ is:

Option 1: n²

Option 2: m²

Option 3: mn

Option 4: 1

Question : In $\triangle ABC$, right angled at B, if $\tan A=\frac{1}{2}$, then the value of $\frac{\sin A(\cos C+\cos A)}{\cos C(\sin C-\sin A)}$ is:

Option 1: $2$

Option 2: $1$

Option 3: $3$

Option 4: $2\sqrt5$

Question : If $\tan \theta=\frac{4}{3}$, then the value of $\frac{3\sin \theta+ 2\cos \theta}{3\sin \theta – 2 \cos \theta}$ is:

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

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

Option 3: $3$

Option 4: $–3$

Question : If $\tan A=\frac{3}{8}$, then the value of $\frac{3 \sin A+2 \cos A}{3 \sin A-2 \cos A}$ is:

Option 1: $-\frac{13}{25}$

Option 2: $-\frac{25}{7}$

Option 3: $\frac{25}{8}$

Option 4: $\frac{13}{21}$