Question

If f(x)=cos*2(x) +sin*4(x)/sin*2(x)+cos*4(x) for all x€R then show that f(2012)=1

Answer 1

Sin²A+cos⁴A

=1-cos²A+(1-sin²A)²

=1-cos²A+1+sin⁴A-2sin²A

=2-2sin²A-cos²A+sin⁴A

=2(1-sin²A)-cos²A+sin⁴A

=2cos²-cos²A+sin⁴A

=cos²A+sin⁴A