Question

Tan 6A = Cot (2A - 22)

Answer 1

Answer:

$\large{\underline{\boxed{\rm A = 14}}}$

Step-by-step explanation:

Given that -

$\rm \tan 6A = \cot (2A - 22)$

We know that -

• tanθ = cot (90° - θ)

$\rm \cot (90 - 6A) = \cot (2A - 22)$

On cancelling cot both sides -

$\rm 90 - 6A = 2A - 22 \\\\\rm - 6A - 2A = - 22 - 90 \\\\ \rm - 8A = - 112 \\\\ \rm A = \frac{112}{8} \\\\ \rm A =14$

Hence, the value of A is 14.

$\rule{300}{2}$

Some more formulas related to the concept are following -

• sin(90° - A) = cosA
• cos(90° - A) = sinA
• tan(90° - A) = cotA
• cot(90° - A) = tanA
• cosec(90° - A) = secA
• sec(90° - A) = cosecA

Answer 2

Answer :-

$\mathsf{A = 14^{\circ}}$

Given :-

$\mathsf {Tan 6A = Cot(2A -22)}$

To find :-

The value of angle A.

Solution:-

$\text{From Trigonometric values at ( 90\pm \theta )}$

we have ,

$\mathsf{Tan \theta = Cot (90-\theta)}$

By using this ,

→$\mathsf{Cot (90-6A) = Cot (2A -22)}$

• Cancelling out cot on both side.

→$\mathsf{90-6A = 2A -22}$

→$\mathsf{90 +22 = 2A + 6A}$

→$\mathsf{112 = 8A}$

→$\mathsf{A = \dfrac{112}{8}}$

→$\mathsf{A = 14^{\circ}}$

• $\text{Some basic concepts}$:-

The Trigonometric ratio change only when angle is :-

$\mathsf{90\pm \theta , 270 \pm \theta }$

The Trigonometric ratio doesn't change when angle is :-

$\mathsf{180\pm \theta , 360\pm \theta }$