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Solve $\sin^{2} x + \cos^{2} y = 2 \sec^{2} z$ for $x, y$ and $z$

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x=(2m+1)π2,m∈Z

y=nπ,n∈Z

z=tπ,t∈Z

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detailed solution

Correct option is D

LHS=sin2x+cos2y≤2, sin2x≤1,cos2y≤1RHS=2sec2z≥2LHS=RHS only when sin2x=1,cos2y=1,2sec2z=2⇒cos2x=0,sin2y=0,cos2z=1⇒cosx=0,siny=0,sinz=0⇒x=(2m+1)π2,y=nπ and z=tπ, m,n,t∈Z

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Solve sin2x+cos2y=2sec2z for x,yand z

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Solve $\sin^{2} x + \cos^{2} y = 2 \sec^{2} z$ for $x, y$ and $z$