If $$sin2A=x$$ then $$sinAsin2Asin3Asin4A$$ is a polynomial in x, the sum of whose coefficients is

Question

If  $$sin2A=x$$ then $$sinAsin2Asin3Asin4A$$ is a polynomial in x, the sum of whose coefficients is

Infinity Learn · Accepted Answer

We have  $$sinAsin2Asin3Asin4A=sinA2sinAcosA3sinA$$−$$4sin3A$$×$$2sin2Acos2A$$                                                                             $$=2sin2AcosA$$×$$sinA3$$−$$4sin2A$$×$$2$$×$$2sinAcosA1$$−$$2sin2A$$                                                                               $$=8sin4Acos2A3$$−$$4sin2A1$$−$$2sin2A$$                                                                               $$=8x21$$−$$x3$$−$$4x1$$−$$2x$$                                                                                $$=24x2$$−$$104x3+144x4$$−$$64x5$$∴ The sum of coefficients $$=$$ $$0$$

If $\sin^{2} A = x$ then $\sin A \sin 2 A \sin 3 A \sin 4 A$ is a polynomial in x, the sum of whose coefficients is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If sin2A=x then sinAsin2Asin3Asin4A is a polynomial in x, the sum of whose coefficients is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If $\sin^{2} A = x$ then $\sin A \sin 2 A \sin 3 A \sin 4 A$ is a polynomial in x, the sum of whose coefficients is