The number of solutions of the equation $$sin3$$⁡ xcos ⁡$$x+sin2$$⁡ $$xcos2$$⁡$$x+$$$$sin$$⁡ $$xcos3$$⁡$$x=1in$$ the interval [$$0$$,$$2$$π] $$is/$$ are

Question

The number of solutions of the equation $$sin3$$⁡ xcos ⁡$$x+sin2$$⁡ $$xcos2$$⁡$$x+$$$$sin$$⁡ $$xcos3$$⁡$$x=1in$$ the interval [$$0$$,$$2$$π] $$is/$$ are

Infinity Learn · Accepted Answer

$$sin3$$⁡xcos⁡$$x+sin2$$⁡$$xcos2$$⁡$$x+$$$$sin$$⁡$$xcos3$$⁡$$x=1or$$  $$sin$$⁡xcos⁡$$xsin2$$⁡$$x+$$$$sin$$⁡xcos⁡$$x+cos2$$⁡$$x=1or$$  $$sin$$⁡$$2x21+$$$$sin$$⁡$$2x2=1or$$  $$sin$$⁡$$2x(2+$$$$sin$$⁡$$2x)=4or$$  $$sin2$$⁡$$2x+2sin$$⁡$$2x$$−$$4=0or$$ $$sin$$⁡ $$2x=$$−$$2$$±$$4+162=$$−$$1$$±$$5This$$ is not possible since −$$1$$≤$$sin$$⁡ $$2x$$≤$$1Hence$$, the given equation has no solution.

The number of solutions of the equation $\sin^{3} x \cos x + \sin^{2} x \cos^{2} x + \sin x \cos^{3} x = 1$ in the interval [0,2 $π$ ] is/ are

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The number of solutions of the equation sin3⁡ xcos ⁡x+sin2⁡ xcos2⁡x+sin⁡ xcos3⁡x=1in the interval [0,2π] is/ are

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The number of solutions of the equation $\sin^{3} x \cos x + \sin^{2} x \cos^{2} x + \sin x \cos^{3} x = 1$ in the interval [0,2 $π$ ] is/ are