Question

सर्वसमिका Cosec2A = 1+ Cot2A को लागू करके इस सिद्ध कीजिए-
(CosA – SinA +1)/ (CosA + SinA -1) = CosecA + CotA)

Answer 1

Answer:

Step-by-step explanation:

Cosec2A = 1+ Cot2A

$\frac{1}{2sinAcosA} = \frac{2sinAcosA + cos^{2} A - sin^2{A} }{2sinAcosA}$

$\Rightarrow 1 = 2sinAcosA + cos^{2} A - sin^{2} A$

Therefore we can write

$\frac{(cos A - sinA + 1)(cosA+sinA +1)}{(cosA + SinA -1)(cosA+sinA+1)} \hspace{0.1cm} = \hspace{0.1cm} \frac{cos^{2}A + cosA - sin^{2}A + cosA + 1 }{2sinAcosA}$

$\Rightarrow \hspace{0.1cm} \frac{2cos^{2}A + 2cosA }{2sinAcosA}$

= cosecA + cotA