Question

If 3 tan A =cot A and A is an acute angle find angle A

Please, I need detailed explaination​

Answer 1

Answer:

A is 30 degrees.

Step-by-step explanation:

cot A = 1/ tan A

Therefore 3 tan A = 1 / tan A

3 tan^2 A = 1

tan^2 A = 1/3

tan A = 1 /√3   is A is acute.

A = 30 degrees.

Answer 2

This is about trigonometric identities.

A = 30°

• In trigonometric identities, we know that;

Tan A = sin A/cos A

Cosec A = 1/sin A

Sec A = 1/cos A

Cot A = 1/tan A

• Now, we are given;

3 tan A = cot A

But we know from above that Cot A = 1/tan A

Thus;

3 tan A = 1/tan A

Rearranging to get;

(tan A)² = 1/3

tan A = √(1/3)

tan A = 1/√3

• Now, from surd form of special angles, we know that;

sin 30° = cos 60° = 1/2

sin 60° = cos 60° = (√3)/2

sin 45° = cos 45° = 1/√2

tan 30° = 1/√3

tan 60° = √3

tan 45° = 1

• Comparing tan A = 1/√3 with the surd forms listed above, we can see that;

A = 30°

A is said to be an acute angle which means it is less than 90° and so it is correct.

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