Question

If A, B and C are the interior angles of a right-angle triangle, right-angled at B then find the value of A, given that tan 2A = cot(A – 30°) and 2A is an acute angle.​

Answer 1

SOLUTION:-

Using the trigonometric ratio of complementary angles,

cot (90°- A) = tan A

From this ratio, we can write the above expression as:

⇒ tan 2A = cot (90°- 2A) ….(1)

Given expression is tan 2A = cot (A – 30°) …(2)

Now, equate the equation (1) and (2), we get

cot (90°- 2A) = cot (A – 30°)

⇒ 90°- 2A = A – 30°

⇒3A = 90° + 30°

⇒3A = 120°

⇒A = 120°/ 3

⇒ A = 40°

More to know about complementary angles

Sin (90∘- θ) = Cos θ

Cos (90∘- θ) = Sin θ

Tan (90∘- θ) = Cot θ

Cosec (90∘- θ) = Sec θ

Sec (90∘- θ) = Cosec θ

Cot (90∘- θ) = Tan θ