Question

If sin 3a=cos(A - 26°) where 3a is an acute angle find the value of A.
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Answer 1

Your answers is given below ~~~~》》》

You should know that , cos(x)=sin(90−x)

hence cos(A−26)=sin(90−A+26)

=sin(116−A)

Now, since 3A is acute,

Hence A is also acute and hence we can directly remove sin function.

$$sin3A = sin(116-A) $

3A=116−A

4A=116

Hence A=29

Answer 2

The value of a = 29°

Step-by-step explanation:

Given :

sin 3A = cos (A − 26°), where 3A is an acute angles

To Find :

The value of A.

Solution :

According to your question:

⇒ Sin 3a = Cos ( a -26 )  

⇒ 3a < 90°

We know :

$\bigstar\;\boxed{\textbf{Sin3A cos(a - 26)}}$

According to formula :  

⇒ Sin3A cos(a - 26)

Now,

Cancelling cos,

⇒ cos(90 − 3a) = cos(a− 26)

⇒ (90 − 3a) = (a − 26)

⇒ 4a = 116°

⇒ a = 29°

∴ The value of a = 29°