Question

Sin 3a=cos(a-26)where 3a is an acute angle find the value of a

Answer 1

Answer :-

a = 29°

Given:-

Sin 3a = Cos ( a -26 )

Where , 3a < 90°

To find :-

The value of a.

Solution :-

As, we know the formula of some compound angle like,

★ $\boxed{\sf{Sin A = Cos(90-A)}}$

Now,

Sin 3a is also written as,

$Sin 3a = Cos (90 -3a )$

Now put the value of Sin 3a,

→$Sin 3a = Cos (a -26)$

→$Cos (90 -3a) = cos (a -26)$

Cancel out Cos,

→$90 -3a = a -26$

→$90 + 26 = a + 3a$

→$116 = 4a$

→$a =\dfrac{116}{4}$

→$a = 29^{\circ}$

Hence,

Now 3a

= 3 × 29

= 87° Ans.

Answer 2

Chapter: 8 - (Introduction to Trignometry)

Class - 10

Answer:

★Value of a = 29°★

Step-by-step explanation:

Given Problem:

Sin 3a = cos(a-26)where 3a is an acute angle find the value of A.

Solution:

To Find:

Value of A

--------------------

Method:

According to your question:

Sin 3a = Cos ( a -26 )  

So, 3a < 90°

We know that,

★SinA = Cos(90 - A)★

According to formula:

⇒Sin3A Cos(90 - A)

Now,

⇒Sin3a = Cos(90 - 3a) = cos(a - 26)

Now, Cancellation of cos,

⇒90 - 3a = a - 26

⇒90 + 26 = a + 3a

⇒116 = 4a

So,

A = 29°

Hence,

The Value of a = 29°