Question

find the value of A if cot3A=tan6A​

Answer 1

Given :

• cot3A = tan6A

To Find :

• The value of A

Concept used :-

• Complementary angle of Trignometry

Formulae used:-

• Cot( 90 - θ) = tanθ

Now,

→ Cot3A = tan6A

→ Cot( 90 - 3A ) = tan6A

→ tan(90 - 3A) = tan6A

→ 90 - 3A = 6A

→ 90 = 6A + 3A

→ 90 = 9A

→ A = 10°

Therefore, The value of A is 10°

Answer 2

Given:

• cot3A = tan6A

To find:

• The value of A

Solution:

$\implies\tt{cot3A=tan6A---(1)}$

As we know that,

$\red{\boxed{\bf{cotA = tan(90-A)}}}$

Here, A is represented as an angle.

Hence, Similarly:

$\red{\boxed{\bf{cot3A = tan(90-3A)}}}$

Let us apply the value of cot3A in -----(1)

$\implies\tt{cot3A=tan6A}$

$\implies\tt{tan(90-3A)=tan6A}$

$\implies\tt{ \cancel{tan}(90-3A)= \cancel{tan}6A}$

$\implies\tt{90-3A=6A}$

$\implies\tt{6A+3A = 90}$

$\implies\tt{9A = 90}$

$\implies\tt{A = \dfrac{90}{9}}$

$\implies\orange{\boxed{\bf{A = 10\degree}}}\checkmark$

Hence, the value of A is 10°.