cos2x=sin3x

Question

question of class 11maths urgently plz

 

Answer 1

cos(2x)=sin(3x),

sin(π/2-2x)=sin(3x),

π/2-2x+2πn=3x, where n is an integer.

5x=π/2+2πn, x=π/10+2πn/5 or 0.1π+0.4πn. (x=0.1π, 0.5π, 0.9π, 1.3π, 1.7π, etc.)

You can see this more clearly by graphing y=cos(2x) and y=sin(3x) and observe where the curves intersect. The symmetry is clear to see.

The red curve is y=cos(2x) and the blue curve is y=sin(3x), and the vertical lines split the domain x into the four quadrants. The symmetry of the five intersections of the two curves is clearly evident, and they have equidistant horizontal spacing of 0.4π as indicated in the above solution.