Question : If $x=\frac{2 \sin \theta}{(1+\cos \theta+\sin \theta)}$, then the value of $\frac{1-\cos \theta+\sin \theta}{(1+\sin \theta)}$ is:

Option 1: $\frac{x}{(1+x)}$

Option 2: $x$

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

Option 4: $\frac{(1+x)}{x}$

Question : If $\operatorname{cos} \theta+\operatorname{sin} \theta=\sqrt{2} \operatorname{cos} \theta$, find the value of $(\cos \theta-\operatorname{sin} \theta)$

Option 1: $\sqrt{2} \sin \theta$

Option 2: $\sqrt{2} \cos \theta$

Option 3: $\frac{1}{\sqrt{2}} \sin \theta$

Option 4: $\frac{1}{2}\cos \theta$

Question : If $\sin \theta+\cos \theta=\sqrt{2} \cos \theta$, then find $\frac{\sin \theta-\cos \theta}{\sin \theta}$:

Option 1: $-\sqrt{2}$

Option 2: $-1$

Option 3: $1$

Option 4: $\sqrt{2}$

Question : If $\cos\theta=\frac{3}{5}$, then the value of $\sin\theta.\sec\theta.\tan\theta$ is:

Option 1: $\frac{9}{16}$

Option 2: $\frac{16}{9}$

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

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

Question : The value of $\frac{2 \cos ^3 \theta-\cos \theta}{\sin \theta-2 \sin ^3 \theta}$ is:

Option 1: $\sec \theta$

Option 2: $\sin \theta$

Option 3: $\cot \theta$

Option 4: $\tan \theta$