show that sin⁴x - cos⁴x = 1 - 2 cos²x
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Answer:
R.HS.=1-2cos²x (to be proved)
L.H.S=sin⁴x-cos⁴x
=(sin²x-cos²x)(sin²x + cos²x) [as,a²-b²=(a+b)(a-b)]
=(sin²x-cos²)*1[as,sin²x+cos²x=1]
=1-cos²x-cos²x [...........do..........]
=1-2cos²x
=R.H.S(PROVED)
Step-by-step explanation:
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