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Without expanding show that: =|cos e c^2...

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

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`cosec^2 theta = 1 + cot^2 theta`
`D= |(1 + cot^2 theta , cot ^2 theta , 1),(cot^2 theta, 1 + cot ^2 theta , -1),(42, 40, 2)|`
`D= 2|(1+cot^2 theta , cot^2 theta ,1),(cot^2 theta , 1 + cot^2 theta , -1),(21, 20, 1)|`
`c_2 -> c_2 + c_3`
`D= 2 | (1 + cot^2 theta , 1+ cot^2 theta , 1),(cot^2 theta ,cot^2 theta , -1),(21,21, 1)|`
`D=0`
Answer
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