Question

sin^4 theta- cos^4 theta =1-2cos^2 theta

Answer 1

(sin⁴A)-(cos⁴A) = 1-2cos²A

LHS => (sin²A)²-(cos²A)²

=> a²-b² = (a+b)(a-b)

=> (sin²A+cos²A)(sin²A-cos²A)

=> as , sin²A+cos²A = 1

=> 1(sin²A-cos²A)

=> sin²A-cos²A

=> adding and subtracting cos²A

=> sin²A-cos²A-cos²A+cos²A

=> (sin²A+cos²A)-2cos²A

=> 1-2cos²A


RHS = 1-2cos²A


since , LHS = RHS

proved ....

hope this helps