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Question

If θϕ=π/2 then show that [cos2θcosθsinθcosθsinθsin2θ][cos2ϕcosϕsinϕcosϕsinϕsinϕ] = 0$

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Solution

θϕ=π4
[cos2θcosθsinθcosθsinθsin2θ][cos2ϕcosϕsinϕcosϕsinϕsin2ϕ]
=[cos2θcosθsinθcosθsinθsin2θ]cos2(π2θ)cos(π2θ)sin(π2θ)cos(π2θ)sin(π2θ)sin2(π2θ)
=[cos2θcosθsinθcosθsinθsin2θ][sin2θsinθcosθsinθcosθcos2θ]
=[sin2θcos2θsin2θcos2θsin2θcos2θsin2θcos2θsin2θcos2θsin2θcos2θsin2θcos2θsin2θcos2θ]
=[0000]=0

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