Prove that cos³A+sin³A/cosA+sinA=1-cosA×sinA
Answers
Answered by
0
Answer: Step-by-step explanation:
L.H.S=\frac{ COS^{3}A+ SIN^{3} A }{COS A+SIN A} + \frac{ COS^{3}A- SIN^{3}A }{COS A-SIN A}
L.H.S= \frac{(COS A-SIN A)( COS^{3}A + SIN^{3}A )+(COS A+SIN A)( COS^{3}A - SIN^{3}A )}{(COS A+SIN A)(COS A-SIN A)}
L.H.S= \frac{2 COS^{4}A-2 SIN^{4}A }{ COS^{2}A- SIN^{2}A }
L.H.S=2 \frac{ ( COS^{2}A) ^{2}- ( SIN^{2}A )^{2} }{COS^{2}A- SIN^{2}A}
L.H.S=2 \frac{ \frac{ (COS 2A+1)^{2} }{ 2^{2} }- \frac{(1-COS 2A)^{2}}{ 2^{2} } }{COS^{2}A- SIN^{2}A}
L.H.S= \frac{ \frac{ COS^{2}2A+1+2COS2A-1- COS^{2}2A+2COS2A }{2} }{COS2A}
L.H.S= \frac{ \frac{4COS2A}{2} }{COS2A}
L.H.S= \frac{2COS2A}{COS2A}
L.H.S=2
L.H.S=R.H.S
hope this helps uh.
please follow me and
please mark my answer as brainliest
Similar questions