Sin²+cos⁴=sin⁴+cos² prove that
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Sin²+cos⁴
L.H.S
=sin²Ө + cos²Ө cos²Ө
=1 - cos² Ө + cos²Ө cos²Ө
=1 - cos² Ө + (1 - sin²Ө)(1 - sin²Ө)
=1 - cos² Ө + 1 - 2sin²Ө + (sinӨ)^4
=sin²Ө + 1 - 2sin²Ө + (sinӨ)^4
=1 - sin²Ө + (sinӨ)^4
=cos²Ө + (sinӨ)^4
=R.H.S
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