Question

IF COS 7 A=SIN(A-6),WHERE 7A IS AN ACUTE ANGLE,FIND THE VALUE OF A.

Answer 1

given cos7A=sin(A-6)

sin(90-7A)=sin(A-6)

since (90-7A) and (A-6) ARE BOTH ACUTE ANGLES

THEREFORE

90-7A=A-6

8A=96

A=12 DEGREES

Answer 2

The value of A = 12°

Correct question : If cos 7A = sin(A - 6°) , where 7A is an acute angle , find the value of A.

Given :

cos 7A = sin(A - 6°) , where 7A is an acute angle

To find :

The value of A

Formula :

sin (90° - θ) = cos θ

Solution :

Step 1 of 2 :

Write down the given equation

Here it is given that ,

cos 7A = sin(A - 6°) , where 7A is an acute angle

Step 2 of 2 :

Find the value of A

cos 7A = sin(A - 6°)

⇒ sin (90° - 7A) = sin(A - 6°) [ ∵ sin (90° - θ) = cos θ ]

⇒ 90° - 7A = A - 6°

⇒ - 7A - A = - 6° - 90°

⇒ - 8A = - 96°

⇒ 8A = 96°

⇒ A = 96°/8

⇒ A = 12°

When A = 12° we have 7A = 84° which is an acute angle

Hence the required value of A = 12°

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