Question

Express sin 5A in terms of Sin A

Answer 1

Sin5A=sin(3A+2A)
=sin3A*cos2A+cos3A*sin2A
=(3sinA-4sin^3 A) *(cos^2 A-sin^2 A) +
(4cos^3A-3cosA)*(2sinA*cosA)

Answer 2

Answer:

$\sin5A= 2\sin A [ 5\sin^4(A) - 4\sin^2(A) - 2]$

Step-by-step explanation:

Express sin 5A in terms of sin A, Using trigonometric identities,

$\sin5A=\sin(3A+2A)$

$\sin5A=\sin(2A)\cos(3A) + \cos(2A)\sin(3A)$

$\sin5A=2\sin A \cos A [4\cos^3(A) - 3\cos A) ]+(3\sin A - 4\sin^3(A))(1- 2\sin^2(A)$

$\sin5A=2\sin A(4\cos^4(A)-3\cos^2(A))+3\sin A-6\sin^3(A)-4\sin^3(A)+8\sin^5(A)$

$\sin5A=2\sin A[4(1- \sin^2(A))^2 -3(1 - \sin^2(A))] - 10\sin^3(A)+8\sin^5(A)$

$\sin5A=2\sin A [1 + \sin^4(A)-2\sin^2(A) - 3 + 3\sin^2(A) - 10\sin^3(A)+8\sin^5(A)$

$\sin5A=2\sin A [\sin^4(A) + \sin^2(A) - 2 ] - 10\sin^3(A)+8\sin^5(A)$

$\sin5A=2\sin^5(A) + 2\sin^3(A) - 4\sin A - 10\sin^3(A)+8\sin^5(A)$

$\sin5A= 10\sin^5(A) - 8 \sin^3(A) - 4\sin A$

$\sin5A= 2\sin A [ 5\sin^4(A) - 4\sin^2(A) - 2]$

$\sin5A= 2\sin A [ 5\sin^4(A) - 4\sin^2(A) - 2]$