Question

Show that
sin^4a-cos^4a=1-2 cos^2a.​

Answer 1

question:-

Sin⁴A-Cos⁴A = 1-2Cos²A

properties to be used:-

• $\huge \fbox \blue{Sin²A+Cos²A=1}$

• $\huge \fbox \blue{Sin²A=1-Cos²A}$

solution:-

LHS

⇒(sin²A)²-(cos²A)²

⇒(sin²A+cos²A)(sin²A-cos²A)

⇒(1)(1-cos²A-cos²A)

⇒(1-2cos²A) = RHS

hence, proved