Question

Prove that:sin^4A×cos^4A÷sinA-cosA=sinA +cosA

Answer 1

Answer:

See the detailed explanation

Step-by-step explanation:

To prove:  $\frac{\sin^4A-\cos^4A}{\sin A-\cos A}=\sin A+\cos A$

$\text{LHS}=\frac{\sin^4A-\cos^4A}{\sin A-\cos A}=\frac{(\sin^2A)^2-(\cos^2A)^2}{\sin A-\cos A}$

       $=\frac{(\sin^2A-\cos^2A)(\sin^2A+\cos^2A)}{\sin A-\cos A}\\=\frac{(\sin A-\cos A)(\sin A+\cos A)(1)}{\sin A-\cos A}\\=\sin A+\cos A=\text{RHS}$

Hence proved

(Note : There is a typo in the question)