Question

proove that :-
(1+cot A)2 + (1-cot A)2 = 2 cosec^2 A​

Answer 1

Answer:

$= (1+\frac{cosA}{sinA} )^2+(1-\frac{cosA}{sinA} )^2\\\\=(\frac{sinA+cosA}{sinA} )^2 +(\frac{sinA-cosA}{sinA} )^2\\=(\frac{sin^2 A+cos^2 A+2sinAcosA}{sin^2 A} )+(\frac{sin^2 A+cos^2 A - 2sinAcosA}{sin^2 A\\} )\\=\frac{sin^2 A+cos^2 A+sinAcosA+sin^2A+cos^2A-2sinAcosA}{sin^2 A} \\=\frac{2(sin^2A+cos^2A)}{sin^2A} \\=\frac{2(1)}{sin^2A} \\=2cosec^2A$