1.

Write the value of 2 (sin6 x + cos6 x) − 3 (sin4 x + cos4 x) + 1.

Answer»

sin6x + cos6x = (sin2x)3 + (cos2x)3

=(sin2x + cos2x)(sin4x+cos4x - sin2xcos2x)

= 1 (sin4x + cos4x – sin2xcos2x)

Substituting above value in given equation

⇒ 2(sin4x + cos4x – sin2xcos2x) - 3(sin4 x + cos4 x) + 1

⇒ 2sin4x + 2cos4x – 2sin2xcos2x – 3sin4x - 3cos4x + 1.

⇒ -sin4x - cos4x - 2sin2xcos2x + 1

⇒ -[(sin2x)+ (cos2x)- 2sin2xcos2x] + 1

⇒ -[( sin2x + cos2x)2] + 1

⇒ -1 + 1

⇒ 0



Discussion

No Comment Found