Find the value of #sin^3A+cos^3A#?

1 Answer
sankarankalyanam
Apr 17, 2018

#color(crimson)((sin A + cos A) * ( 1 - (sin2A) / 2)#

Explanation:

#sin^3 A + cos^3 A#

We know, #a^3 + b^3 = (a + b) * (a^2 - ab + b^2)#

#:. => (sin A + sin B) * (sin^2 A - sin A cos A + cos^2 A)#

#=> (sin A + cos A) * ( 1 - sin A cos A), " as " color(red)((sin^2 A + cos^2 A = 1)#

#=>(sin A + cos A) * ( 1 - (sin 2A) / 2), " being " color(red)((sin 2A = 2 sin A cos A)#

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