if cot A = 3 tan A. then the measure of the angle A is.

Question

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

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Answer 1

Hello,
Given
cot A = 3 tan A

We know that
cot A = 1 / tan A

So,
1 / tan A = 3 tan A

Multiply both sides by tan A:
1 = 3 tan²A

tan²A = 1 / 3

tan A = 1 / √3

The angle whose tangent is 1 / √3 is 30°.

So, the measure of angle A is 30°.

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if cot A = 3 tan A. then the measure of the angle A is.

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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: 4Option 2: 2Option 3: 3Option 4: 6

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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