Without expanding show that: `=|cos e c^2thetacot^2theta1cot^2thetacos e c^2theta-1 42 40 2|=0`

Without expanding show that: =|cos ec^(2)theta cot^(2)theta1cot^(2)theta cos ec^(2)theta-142402|=0

Without expanding show that: = |(cose c^2theta,cot^2theta,1),(cot^2theta,cosec^2theta,-1) ,(42 ,40, 2)| =0

Without expanding show that: =|[cose c^2theta,cot^2theta,1],[cot^2theta,cosec^2theta,-1],[ 42, 40, 2]|=0

Without expanding show that: cosec theta,cot^(2)theta,1cot^(2)theta,csc^(2)theta,-142,40,2]|=0

Prove: cos e c^6theta=cot^6theta+3cot^2thetacos e c^2theta+1

Without expanding, show that : Delta = {:|(cosec^2theta,cot^2theta,1),(cot^2theta,cosec^2theta,-1),(42,40,2)|=0

Prove: cos e c^2theta+sec^2theta=cos e c^2thetasec^2theta

Prove that cos^2theta+cos^2thetacot^2theta=cot^2theta

Prove: tan^2thetacos^2theta=1-cos^2theta

what is value of: |[cosec^2theta,cot^2theta,1],[cot^2theta,cosec^2theta,-1],[42,40,2]| ?