Question

If tan 2a =cot(a-18) where 2a is on actue angle then find the value of a

Answer 1

Question:-

➡ If tan(2x) = cot(x - 18°) where 2x is an acute angle, find the value of x.

Answer:-

➡ The value of x is

Solution:-

Given that,

➡ tan(2x) = cot(x - 18°)

We know that, cot(90° - x) = tan(x)

So,

➡ cot(90° - 2x) = cot(x - 18°)

➡ 90° - 2x = x - 18°

➡ x + 2x = 90° + 18°

➡ 3x = 108°

Dividing both sides by 3, we get,

➡ x = 36°

Hence, the value of x is 36°

Formulae used:-

➡ cot(90° - x) = tan(x)

➡ tan(90° - x) = cot(x)

Other Formulae:-

➡ sin(90° - x) = cos(x) for 0 ⩽ x ⩽ 90°

➡ cos(90° - x) = sin(x) for 0 ⩽ x ⩽ 90°

➡ sin²(x) + cos²(x) =1 for 0 ⩽ x ⩽ 90°

Answer 2

Answer:

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