Where is $\cos$ positive?

Question : $\frac{\sin ^2 \theta}{\cos \theta(1+\cos \theta)}+\frac{1+\cos \theta}{\cos \theta}=$?

Option 1: $\operatorname{cosec}\theta$

Option 2: $\sec\theta$

Option 3: $2\cos\theta$

Option 4: $2\sec\theta$

Question : The value of $\sec x - \cos x = $?

Option 1: $\tan x \sin x$

Option 2: $\sec x \tan x$

Option 3: $\tan x \cos x$

Option 4: $\sec x \cos x$

Question : $\frac{\cos \theta}{\sec \theta-1}+\frac{\cos \theta}{\sec \theta+1}$ is equal to :
 

Option 1: $2 \sec ^2 \theta$

Option 2: $2 \cot ^2 \theta$

Option 3: $2 \cos ^2 \theta$

Option 4: $2 \sin ^2 \theta$