sec⁴A-sec²A=tan⁴A+tan²A
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Answer:
Sec⁴A-Sec²A=Tan⁴A+Tan²A
Step-by-step explanation:
RHS=Tan²A+Tan²A=(SinA/CosA)⁴ +(SinA/CosA)²
=Sin⁴A/Cos⁴A +Sin²A/Cos²A=(Sin²A.Sin²A)/Cos⁴A +Sin²A/Cos²A=(1-Cos²A)²/Cos⁴A +(1-Cos²A)/Cos²A
=(1-2Cos²A+Cos⁴A)/Cos⁴A + 1/Cos²A -1
=1/Cos⁴A -2/Cos²A +1 +Sec²A -1=Sec⁴A -2Sec²A+Sec²A
=Sec⁴A-Sec²A
₀⁰₀ LHS=RHS
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