Given that sin(5x-28)degree=cos(3x-5),0 lessthan x lessthan 90degree,find the value of x.

If sin A = cos B, A and B must be complementary angles (if both are less than 90 degrees).

That means
5x - 28 + 3x -5 = 90 degrees
8x = 123
x = 15.375 degrees
Check: sin (5x-28) = sin 48.875 = 0.753276
cos (3x-5) = cos 41.125 = 0.753276

There might be other solutions for which 5x-28 exceeds 90 degrees. Check it out

To solve the equation sin(5x - 28)° = cos(3x - 5) for 0° ≤ x ≤ 90°, we can use trigonometric identities to simplify the equation.

1. Recall that sin(x) = cos(90° - x). We can rewrite the equation as:
sin(5x - 28)° = sin(90° - (3x - 5))

2. Since the sine function is equal for two angles if the two angles themselves are equal or supplementary (add up to 180°), we have:
5x - 28 = 90° - (3x - 5) or 5x - 28 = 180° - (3x - 5)

3. Solve the first equation:
5x - 28 = 90° - 3x + 5

Simplify and rearrange terms:
5x + 3x = 90° + 5 + 28
8x = 123°
x = 123° / 8
x ≈ 15.375°

4. Check the solution:
sin(5x - 28)° = sin(5 * 15.375 - 28)° ≈ sin(68.125)° ≈ 0.934
cos(3x - 5) = cos(3 * 15.375 - 5) ≈ cos(40.125) ≈ 0.934

The values are approximately equal, confirming that x ≈ 15.375° is a valid solution within the specified range.

To find the value of x, we need to solve the equation sin(5x - 28°) = cos(3x - 5°) within the given range of 0° to 90°.

First, let's convert the equation to use the same trigonometric function. We know that sin(x) = cos(90° - x), so we can rewrite the equation as sin(5x - 28°) = sin(90° - (3x - 5°)).

Using the property of equality for sine functions, we set the expressions inside the sin functions equal to each other:

5x - 28° = 90° - (3x - 5°).

Simplifying this equation, we remove the parentheses on the right side:

5x - 28° = 90° - 3x + 5°.

Next, we combine like terms by adding 3x to both sides of the equation:

5x + 3x - 28° = 90° + 5°.

This gives us:

8x - 28° = 95°.

Now we isolate the variable x by adding 28° to both sides:

8x = 123°.

Finally, divide both sides by 8 to solve for x:

x = 123° / 8.

Therefore, the value of x is approximately 15.4°.