Question

Sin3x=cos4x. .…………………

Answer 1

Sin3x-sin(π/2-4x)=0
2sin(7x/2-π/4)cos(π/4-x/2)=0
sin(7x/2-π/4)=0⇒7x/2-π/4=πn⇒7x/2=π/4+πn⇒x=π/14+2πn/7
cos(π/4-x/2)=0⇒sin(x/2+π/4)=0⇒x+π/4=πn⇒x/2=-π/4+πn⇒x=-π/2+2πn

Answer 2

To solve the equation sin(3x) = cos(4x), we can use the trigonometric identity sin(x) = cos(π/2 - x). Applying this identity, we have:

sin(3x) = cos(4x) sin(3x) = cos(π/2 - 4x)

Now, we can equate the angles inside the trigonometric functions:

3x = π/2 - 4x

Let's solve for x:

3x + 4x = π/2 7x = π/2 x = π/14

So, the solution to the equation sin(3x) = cos(4x) is x = π/14.