Question

Prove cot sqaureA
+ 1 = cosec squareA

Answer 1

Answer:

HEYY MATE..

as we know,cose^2A-cot^2A=1

So,cosec^2A=1+cot^2A

hope it helps..❤..

Answer 2

$\huge{\bold{ Solution}} \\ \\ {\red{\huge{\underline{\mathbb{To \: prove:-}}}}} \\ \\1 + {cot}^{2}A = {cosec}^{2} A \\ \\ {\red{\huge{{\mathbb{Proof:-}}}}} \\ \\ \small{\bold{ L \: H \: S}} \\ = 1 + {cot}^{2} A \\ \\ = 1 + \frac{ {cos}^{2}A }{ {sin}^{2} A} \\ \\ = \frac{ {sin}^{2}A + {cos}^{2} A}{ {}^{ {sin}^{2} A} } \\ \\ = \frac{1}{ {sin}^{2} A} \\ \\ = {cosec}^{2} A = RHS \: \\ \\ LHS = RHS\\ \\ {\blue{\small{\underline{\mathbb{Hence \: proved}}}}} \\ \\ \huge{\small{ Trigonometry \: identities \: used \: }} \\ \\ 1. \: {cot}^{2} \theta = \frac{ {cos}^{2} \theta}{ {sin}^{2} \theta } \\ \\ 2. \: {sin}^{2} \theta \: + {cos}^{2} \theta = 1 \\ \\ 3. \: \frac{1}{ {sin}^{2} \theta } = {cosec}^{2} \theta$