Please help me solve
sin3x=cos(5x+10°)
since sin(x) = cos(90-x), you have
sin3x = sin(80-5x)
3x = 80-5x
x = 10
and sure enough, sin30° = cos60°
To solve the equation sin(3x) = cos(5x + 10°), we can use the trigonometric identity:
sin(θ) = cos(90° - θ)
Applying this identity, we have:
sin(3x) = cos(90° - (5x + 10°))
sin(3x) = cos(80° - 5x)
Now, we can equate the angles inside the trigonometric functions:
3x = 80° - 5x
Combining like terms:
8x = 80°
Dividing by 8:
x = 10°
Therefore, the solution to the equation sin(3x) = cos(5x + 10°) is x = 10°.
To solve the equation sin(3x) = cos(5x + 10°), we can use trigonometric identities and algebraic manipulation.
First, let's rewrite the equation using the identity cosθ = sin(90° - θ):
sin(3x) = sin(90° - (5x + 10°))
According to this identity, sin(90° - θ) is equal to cosθ. So, we can rewrite the equation as:
sin(3x) = cos(5x + 10°)
cos(5x + 10°) = sin(3x)
Now, we know that two trigonometric functions are equal when their arguments are equal, so we can set the arguments of sin and cos equal to each other:
5x + 10° = 90° - 3x
Now, solve for x:
5x + 10° = 90° - 3x
Add 3x to both sides:
5x + 3x + 10° = 90°
Combine like terms:
8x + 10° = 90°
Subtract 10° from both sides:
8x = 90° - 10°
8x = 80°
Divide both sides by 8:
x = 80° / 8
x = 10°
So, the solution to the equation sin(3x) = cos(5x + 10°) is x = 10°.