Question

(1+cotA)²+(1-cotA)²=2cosec²A

Answer 1

Answer:

Step-by-step explana.

1 + cot square + 2 cot a + 1 + cot square a - 2 cot a equals to 2 cosec square a.

2 + 2 cos square a equals to 2 in bracket 1 + cot square a bracket close.

Equals to 2 cos square a hence prove.

Answer 2

(1+cotA)^2 + (1-cot)^2

$\sf \: opening \: the \: brackets \: using \: identity \: \\ \sf {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \: and \\ \sf {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$


= 1 + cot^2 A +2cotA + 1 +cot^2 A - 2 cotA

$\sf \: 2cot \: a - 2cot \: a = 0$
So,

= 2 +2cot^2 A

=2(1+cot^2 A)

⏩ Using identity 1+cot^2 A = cosec^2 A

=2 cosec^2 A

= LHS

Hence Proved


$\boxed{ \bf{some \: identities}}$


⏩Sin^2 A + Cos^2A =1

⏩ 1 + Tan^2 A = Sec^2 A

⏩ 1+ Cot^2 A = Cosec^2 A