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CBSE Class 10 Answered

2(sin^6 A+cos^6 A)-3(sin^4 A+cos^4 A)+1=0
Asked by | 29 Aug, 2012, 09:17: PM
answered-by-expert Expert Answer

SIN6 A + COS 6A IS IN FORM OF A3 + B3

SIN6A+ COS 6 A = ( SIN 2 A + COS 2A ) 3 - 3 SIN2A * COS2A ( SIN 2A + COS 2A )

=> 13 - 3 SIN2A * COS2A

ALSO SIN4A + COS 4A IS IN FORM OF A2 + B2

SIN4A + COS 4A = ( SIN 2A + COS 2A)2 - 2 ( SIN 2A * COS 2A)

=> 1 2 - 2 ( SIN 2A * COS 2A)

Now, LHS = 2(sin6A + cos6A) - 3(sin4 + cos4) +1 =

2 (13 - 3 SIN2A * COS2A ) - 3 ( 1 2 - 2 SIN 2A * COS 2A) + 1

= 2 - 6 SIN 2A * COS 2A - 3 + 6 SIN 2A * COS 2A + 1

= 0

Answered by | 29 Aug, 2012, 11:36: PM

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