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L

lp_qt

$ sina.\cos ^3 a - \sin^3 a. cosa =\dfrac{1}{2}.\sin2a.\cos^2a-\dfrac{1}{2}.\sin2a.\sin^2a$

$=\dfrac{1}{2}.\sin2a(\cos^2a-\sin^2a)=\dfrac{1}{2}.\sin2a(\cos^2a-\sin^2a)=\dfrac{1}{2}.\sin2a.\cos2a=\dfrac{1}{4}.\sin4a$
 
L

lp_qt

$sin^6a+cos^6a=(sin^2a+cos^2a)^3-3.sin^2a.cos^2a(sin^2+cos^2a)
=1-3.\dfrac{1}{4}.sin^22a=1-3.\dfrac{1}{4}.\dfrac{1-cos4a}{2}=\dfrac{5+3.cos4a}{8}$
 
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