prove that. Sin5A = 16Sin^5A - 20Sin^3A+5SinA
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Step-by-step explanation:
sin5A=sin(3A+2A)
= sin3Acos2A+cos3Asin2A
=(3sinA-4sin^3A)(1-2sin^A)+(4cos^3-3cosA)2sinAcosA
=3sinA-6sin^3A-4sin^3A+8sin^5A+ (4cos^2A-3)2sinAcos^2A
=3sinA-6sin^3A-4sin^3A+8sin^5A+ [4(1-sin^2A)-3]2sinA(1-sin^2A)
=3sinA-6sin^3A-4sin^3A+8sin^5A+ (4-4sin^2A-3)(2sinA-2sin^3A)
=3sinA-6sin^3A-4sin^3A+8sin^5A+ (1-sin^2A)(2sinA-2sin^3A)
=3sinA-10sin^3A+8sin^5A+2sinA- 2sin^3A-8sin^3A+8sin^5A
=5sinA-20sin^3A+16sin^5A
=RHS
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