Question

5. sin^4 A - cos^4 A = 2 sinA-1. 10 grade​

Answer 1

Answer:

See the explanation

Step-by-step explanation:

$\text{LHS}=\sin^4A-\cos^4A$

       $=(\sin^2A)^2-(\cos^2A)^2\\=(\sin^2A+\cos^2A)(\sin^2A-\cos^2A)$  $\boxed{\because a^2-b^2=(a+b)(a-b)}$

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

      $=\sin^2A-1+\sin^2A\\=2\sin^2A-1=\text{RHS}$

Hence proved