3(sinO+cosO)-(sinO+cosO)³ = 2(sin³O + cos³O)
Answers
Answered by
56
QUESTION
TO PROVE
3(sinø+cosø)-(sinø+cosø)³ = 2(sin³ø+ cos³ø)
ANSWER
LHS
3(sinø+cosø)-(sinø+cosø)³
=(sinø+cosø)[3-(sinø+cosø)²]
=(Sinø +Cosø)[3-(sin²ø+cos²ø+2sinø cosø)]
=(Sinø +Cosø)[3-(1+2sinø cosø)]
=(Sinø +Cosø)[2-2sinø cosø]
=2(Sinø +Cosø)[1-sinø cosø]
=2(Sinø +Cosø)[sin²ø+cos²ø-sinø cosø]
=2(sin³ø+cos³ø)
(as [a+b][a²+b²-ab]=a³+b³)
RHS
=2(sin³ø+cos³ø)
THEREFORE LHS=RHS
(VERIFIED)
Answered by
5
Answer:
above anser is absolutely ryt....
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