Question

6. If sin 3 A = cos (A -10°), where 3A is an acute angle then find ZA.
[CBSE 2016]​

Answer 1

Step-by-step explanation:

sin3@=cos(90-3@)

cos(90-3@)=cos(@-10)

90-3@=@-10

4@=100

@=25°

Answer 2

Required Answer:-

Given:

• sin 3A = cos(A - 10°), 0° ≤ A ≤ 90°

To Find:

• The value of A.

Solution:

Given that,

→ sin 3A = cos(A - 10°)

We know that,

→ cos(90° - x) = sin(x)

→ cos(90° - 3A) = sin 3A

Therefore,

→ cos(90° - 3A) = cos(A - 10°)

Comparing both sides, we get,

→ 90° - 3A = A - 10°

→ 90° + 10° = 4A

→ 4A = 100°

Dividing both sides by 4, we get,

→ A = 25°

★ Therefore, the value of A is 25°.

Answer:

• A = 25°

More Formulae:

• sin(90° - x) = cos(x) and cos(90° - x) = sin(x)
• cosec(90° - x) = sec(x) and sec(90° - x) = cosec(x)
• tan(90° - x) = cot(x) and cot(90° - x) = tan(x)
• sin²x + cos²x = 1
• cosec²x - cot²x = 1
• sec²x - tan²x = 1