Question

Cot²A-cos²A=cot²A.cos²A​

Answer 1

$\large\underline{\boxed{\frak Answer }}$

$:\leadsto \sf \cot^{2} A-\cos^{2} A$

$:\leadsto \sf\dfrac{\cos^{2}A }{\sin^{2} A} -\cos^{2} A$

$:\leadsto\sf \dfrac{\cos^{2}A-\cos^2A.\sin^2A }{\sin^2A}$

$:\leadsto \sf\dfrac{\cos^2A(1-\sin^2A)}{\sin^2A}$

We know that:-

• ${\underline{\boxed{\sf \cos^2A=1-sin^2A }}}$

$:\leadsto\sf\dfrac{\cos^2A(\cos^2A)}{\sin^2A}$

$:\leadsto\sf \dfrac{\cos^2A}{\sin^2A}.\cos^2A = \bf\red{\cot^2A.\cos^2A}$

I hope it's helpful :D