# If Tan 2 a = Cot (A − 12°), Where 2 a is an Acute Angle, Find the Value of A. - Mathematics

Sum

If tan 2 A = cot (A − 12°), where 2 A is an acute angle, find the value of A.

#### Solution

$\begin{array}{l}sin3A = \cos(A - {26}^\circ ) \\ \end{array}$
$\begin{array}{l}\Rightarrow cos( {90}^\circ - 3A) = \cos(A - {26}^\circ )[ \because \sin\theta = \cos( {90}^\circ- \theta)] \\ \end{array}$
$\begin{array}{l}\Rightarrow {90}^\circ- 3A = A - {26}^\circ \\ \end{array}$
$\begin{array}{l}\Rightarrow {116}^\circ = 4A \\ \end{array}$
$\Rightarrow A = \frac{{116}^\circ}{4} = {29}^\circ$

Concept: Trigonometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 7 Trigonometric Ratios of Complementary Angles
Exercise | Q 13 | Page 314