Evaluate:- sin^6 theta - cos^6 theta
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Step-by-step explanation:
= sin⁶a- cos⁶a
= (sin²a)³ - (cos²a)³
= (sin²a -cos²a) (sin²a+cos²a+2sin²acos²a)
= (sin²a-cos²a) (1+2sin²acos²a)
= (sin²a-cos²a)(sin4a+cos4a). if a=30⁰
=( 1)(sin4(30)+cos4(30))
= sin120+cos120
=sin(90+30) + cos(90+30)
=cos30+sin30
=√3/2 +1/2
=√3+1/2
=1.732+1/2
=2.7/2
approximately =~ 1
sin⁶a+cos⁶a~=1
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