Question : If $\sec 3 {x}=\operatorname{cosec}\left(3 {x}-45^{\circ}\right)$, where $3x$ is an acute angle, then ${x}$ is equal to:

Option 1: $45^{\circ}$

Option 2: $22.5^{\circ}$

Option 3: $35^{\circ}$

Option 4: $27.5^{\circ}$

Question : If $3\left(\cot ^2 \theta-\cos ^2 \theta\right)=1-\sin ^2 \theta, 0^{\circ}<\theta<90^{\circ}$, then $\theta$ is equal to:

Option 1: $30^{\circ}$

Option 2: $60^{\circ}$

Option 3: $45^{\circ}$

Option 4: $15^{\circ}$

Question : If $(\cos \theta+\sin \theta):(\cos \theta-\sin \theta)=(\sqrt{3}+1):(\sqrt{3}-1), 0^{\circ}<\theta<90^{\circ}$, then what is the value of $\sec \theta$?

Option 1: 2

Option 2: $\sqrt{2}$

Option 3: 1

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

Question : If $\frac{\cos ^2 \theta}{\cot ^2 \theta–\cos ^2 \theta}=3$, where $0^{\circ}<\theta<90^{\circ}$ then the value of $\theta$ is:

Option 1: $45^{\circ}$

Option 2: $50^{\circ}$

Option 3: $60^{\circ}$

Option 4: $30^{\circ}$

Question : Find the value of $\frac{\sin ^2 39^{\circ}+\sin ^2\left(90^{\circ}–39^{\circ}\right)}{\cos ^2 35^{\circ}+\cos ^2\left(90^{\circ}–35^{\circ}\right)}+3 \tan 25^{\circ} \tan 75^{\circ}$:

Option 1: 2

Option 2: 4

Option 3: 3

Option 4: 1