Question

pls help honestly m inside the exam

Answer 1

Hi.

Here is your answer---

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To Prove---
 
       Cos^4 A - Sin^4 A = 1 - 2Sin^2 A
 
From L.H.S.

      (Cos^2 A)^2 - (Sin^2 A)^2 
   = (Cos^2 A - Sin^2A)(Cos^A +Sin^2A)        [Since,a^2 - b^2 = (a +b)(a -b)]  
   =  (Cos^2 A - Sin^2 A)(1)                       [Since, Sin^2 A + Cos^2 A = 1]
   =  (1 - Sin^2 A - Sin^2 A)                        [ Since Cos^2A = 1 - Sin^2 A]
   = 1 - 2 Sin^2A
   = L.H.S.
 
   Hence Proved.

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Hope it helps.

Have a nice day.