Question

prove:sin⁴ thita-cos⁴thita=1-1-2cos²thita​

Answer 1

Answer:

Step-by-step explanation:

1.    $sin^{4}A-cos^{4}A=1-2cos^{2} A$

L.H.S:-  $sin^{4}A-cos^{4}A$

          $=(sin^{2} A)^{2} -(cos^{2} A)^{2}$

          $=(sin^{2}A+cos^{2}A)(sin^{2}A-cos^{2}A)$

          $=(1) (sin^{2} A-cos^{2} A+cos^{2} A-cos^{2} A)$

          $=(sin^{2} A+cos^{2} A-2cos^{2} A)$

          $=1-2cos^{2} A$

           L.H.S = R.H.S

           Hence proved.

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