((sin(x))/(√(2sin^2 (x)+cos^2 (x)))) +(1/(√2))=csc(x)(√(2sin^2 (x)+cos^2 (x))) show that x={(π/2)+2πn} and x={cos^(−1) ((√3))−π+2πn} and x={−cos^(−1) ((√3))+2πn}


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Question Number 84002 by M±th+et£s last updated on 08/Mar/20
$((sin(x))/(√(2sin^2 (x)+cos^2 (x)))) +(1/(√2))=csc(x)(√(2sin^2 (x)+cos^2 (x))) show that x={(π/2)+2πn} and x={cos^(−1) ((√3))−π+2πn} and x={−cos^(−1) ((√3))+2πn}$
$\frac{s i n (x)}{\sqrt{2 {s i n}^{2} (x) + {c o s}^{2} (x)}} + \frac{1}{\sqrt{2}} = c s c (x) \sqrt{2 {s i n}^{2} (x) + {c o s}^{2} (x)}$ $s h o w t h a t$ $x = {\frac{π}{2} + 2 π n} a n d x = {{c o s}^{- 1} (\sqrt{3}) - π + 2 π n}$ $a n d x = {- {c o s}^{- 1} (\sqrt{3}) + 2 π n}$
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