Question

(1+cotA)² +(1-cotA)²=2cosec²A​

Answer 1

Answer:

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

\begin{gathered}\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\end{gathered}

openingthebracketsusingidentity

(a+b)

2

=a

2

+b

2

+2aband

(a−b)

2

=a

2

+b

2

−2ab

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

\sf \: 2cot \: a - 2cot \: a = 02cota−2cota=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}}

someidentities

⏩Sin^2 A + Cos^2A =1

⏩ 1 + Tan^2 A = Sec^2 A

⏩ 1+ Cot^2 A = Cosec^2 A