Prove That:-
Sin⁴thita - cos⁴thita = 1-2cos²thita.
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Answered by
1
Step-by-step explanation:
sin⁴A-cos⁴A=(sin²)²A-(cos²)²A
since a²-b²=(a+b)(a-b)
therefore
sin⁴A-cos⁴A=(sin²A+cos²)(sin²-cos²)
=1(1-cos²-cos²)
=1-2cos²A...hence proved
Answered by
1
Step-by-step explanation:
LHS
Sin⁴θ-Cos⁴θ
=(Sin²θ)²-(Cos²θ)²
=(Sin²θ+Cos²θ)(Sin²θ-Cos²θ)
=1(Sin²θ-Cos²θ)
=Sin²θ-Cos²θ
=1-Cos²θ-Cos²θ {∵Sin²θ=1-Cos²θ}
=1-2Cos²θ
=RHS
PROVED
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