Question

can someone please solve this question and give the explanation . i request no spammers ​

Answer 1

Answer:

Given

sinA + cosecA = 2

Squaring  on both sides

(sinA + cosecA)² = 2²

sin^2A + cosec^2A + 2 sinA cosecA = 4

sin^2A + cosec^2A = 4 - 2 sinAcosecA

WKT cosec A = 1/sinA

sin^2A + cosec^2A = 4 -2 

∴ sin^2A + cosec^2A = 2

Answer 2

$\sin( \alpha ) + \csc( \alpha ) = 2 \\ \\ \sin( \alpha ) + \frac{1}{ \sin( \alpha ) } = 2 \\ \\ \frac{ { \sin}^{2} \alpha + 1 }{ \sin( \alpha ) } = 2 \\ \\ { \sin }^{2} \alpha + 1 - 2 \sin( \alpha ) = 0 \\ \\ { (\sin( \alpha ) + 1) }^{2} = 0 \\ \\ \sin( \alpha ) = 1 \\ \\ \csc( \alpha ) = \frac{1}{ \sin( \alpha ) } = \frac{1}{1} \\ \\{ \sin}^{n} \alpha + { \csc}^{n} \alpha = \\ \\ 1 + 1= 2$

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