Question

show that 3(sin o -cos o)^4 + 6(sin o +cos o )^2 +4(sin^6 o+cos^6 o) is independent of o.

Answer 1

3 (0-1)^4 + 6 (0+1)^2+4 (0^6+1^6)
3 + 6 +4
13.
hope it helps

Answer 2

Given :

3 ( sin o - cos o )⁴ + 6 ( sin o + cos o )² + 4 ( sin⁶ o + cos⁶ o )

= > 3 ( sin² o + cos² o - 2 sin o cos o )² + 6 ( sin² o + cos² o + 2 sin o cos o ) + 4 ( sin² o + cos² o )( sin⁴o + cos⁴o - sin²o cos²o )

= > 3 ( 1 - 2 sin o cos o )² + 6 ( 1 + 2 sin o cos o ) + 4 [ ( sin² o + cos² o )² - 3 sin²o cos²o ) ]

= > 3 ( 1 + 4 sin² o cos² o - 4 sin o cos o ) + 6 + 12 sin o cos + 4 - 12 sin²o cos²o

= > 3 + 12 sin² o cos² o - 12 sin² o cos² o + 6 + 12 sin o cos o + 4 - 12 sin o cos o

= > 6 + 4 + 3

= > 13

Hence it does not depend on o.

Any value of "o" will result in 13 .

Always sin² o + cos² o = 1