The expression 3[ sin 4((3/2) π-α)+ sin 4(3 π+α)] -2[ sin 6((1/2) π+α)+ sin 6(5 π-α)] is equal to

Question

The expression 3[ sin 4((3/2) π-α)+ sin 4(3 π+α)] -2[ sin 6((1/2) π+α)+ sin 6(5 π-α)] is equal to (A) 0 (B) 1 (C) 3 (D) None of these

Tardigrade Admin · Accepted Answer

3[ sin 4((3/2) π-α)+ sin 4(3 π+α)]-2 [ sin 6((1/2) π+α)+ sin 6(5 π-α)] =3( cos 4 α+ sin 4 α)-2( cos 6 α+ sin 6 α) =3(1-2 sin 2 α cos 2 α)-2[( sin 2 α+ cos 2 α)3. .-3 sin 2 α cos 2 α( sin 2 α+ cos 2 α)] =3(1-2 sin 2 α cos 2 α)-2[1-3 sin 2 α cos 2 α] =1

Q. The expression 3[sin4(23​π−α)+sin4(3π+α)] −2[sin6(21​π+α)+sin6(5π−α)] is equal to

0

1

3

None of these

3[sin4(23​π−α)+sin4(3π+α)]−2 [sin6(21​π+α)+sin6(5π−α)] =3(cos4α+sin4α)−2(cos6α+sin6α) =3(1−2sin2αcos2α)−2[(sin2α+cos2α)3 −3sin2αcos2α(sin2α+cos2α)] =3(1−2sin2αcos2α)−2[1−3sin2αcos2α] =1

Q. The expression $3 [sin^{4} (\frac{3}{2} π - α) + sin^{4} (3 π + α)]$ $- 2 [sin^{6} (\frac{1}{2} π + α) + sin^{6} (5 π - α)]$ is equal to