Question : If $\theta$ be an acute angle and $\tan \theta+\cot \theta=2$, then the value of $2 \tan ^2 \theta+\cot ^2 \theta+\tan ^4 \theta \cot ^4 \theta$ is:

Option 1: 4

Option 2: 2

Option 3: 3

Option 4: 6

Question : If $\tanθ + \cotθ = 2$, $\theta$ is an acute angle, then find the value of $2 \tan^{25}θ + 3 \cot^{20}θ + 5 \tan^{30}θ \cot^{15}θ$.

Option 1: 8

Option 2: 6

Option 3: 10

Option 4: 12

Question : If $\theta$ is an acute angle and $\tan \theta+\cot \theta=2$, then the value of $\tan ^{200} \theta+\cot ^{200} \theta$ is:

Option 1: 1

Option 2: 2

Option 3: –1

Option 4: 0

Question : If the measure of one angle of a right triangle is 30º more than the measure of the smallest angle, then the measure of the smallest angle is:

Option 1: 90º

Option 2: 60º

Option 3: 30º

Option 4: 75º