Question

Fin the value of x in

Sin 60°=cos (3x-45)°given that 0°≤x≤πc/2

Answer 1

[AI-generated answer — Bot]

To find the value of x, we need to solve the equation:

Sin 60° = Cos(3x - 45)°

First, let's simplify the equation:

Sin 60° = Cos(3x - 45)°

Since Sin 60° = 1/2, we can substitute this:

1/2 = Cos(3x - 45)°

To find the value of x, we need to isolate the variable. Let's rearrange the equation:

Cos(3x - 45)° = 1/2

Now, we can take the inverse cosine (or arccos) of both sides to get rid of the cosine function:

3x - 45 = arccos(1/2)

Since 0° ≤ x ≤ π/2, x can be in the first or second quadrant. In both quadrants, the cosine function is positive, so we can rewrite the equation as:

3x - 45 = arccos(1/2)

We know that the cosine of 60° is equal to 1/2, so the arccos of 1/2 is 60°:

3x - 45 = 60°

Now, let's solve for x:

3x = 60° + 45

3x = 105°

x = 105° / 3

x = 35°

Therefore, the value of x is 35°.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the value of x, we can start by using the identity that sin(60°) = cos(90° - 60°). Therefore, sin(60°) = cos(30°).

So, we have:

cos(30°) = cos(3x - 45)°

Since we are given that 0° ≤ x ≤ π/2, we can solve for x.

First, we need to write the equation as an angle between 0° and 90°.

To do this, we can equate the angles:

30° = 3x - 45°

Now, let's solve the equation for x:

3x - 45° = 30°

Add 45° to both sides:

3x = 30° + 45°

3x = 75°

Divide both sides by 3:

x = 75° / 3

x = 25°

Therefore, the value of x is 25°.