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Which of the following determinants(s) v...

Which of the following determinants(s) vanish(es)? `|4 1 2 10 2 5 3 4 3//2|` (b) `|1 1 1sin^2thetasin^2 2thetasin^2 3thetacos^2thetacos^2 2thetacos^2 3theta|` `|1 1 1 1 2 3 1-2-3|` (d) `|log2log3-log6i-2i i^(2009)2+sqrt(3)1+sqrt(12)-3-sqrt(27)|`

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Prove that sin^6theta+cos^6theta=1-3sin^2thetacos^2theta

Prove the following identity: (1/(sec^2theta-cos^2theta)+1/(cos e c^2theta-sin^2theta))sin^2thetacos^2theta=(1-sin^2thetacos^2theta)/(2+sin^2thetacos^2theta)

Prove the following identity: (1/(sec^2theta-cos^2theta)+1/(cos e c^2theta-sin^2theta))sin^2thetacos^2theta=(1-sin^2thetacos^2theta)/(2+sin^2thetacos^2theta)

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show that cos2thetacos(theta/2)-cos3thetacos((9theta)/2)=sin5thetasin((5theta)/2)

Prove the following identity: (tan^3theta)/(1+tan^2theta)+(cot^3theta)/(1+cot^2theta)=(1-2sin^2thetacos^2theta)/(sintheta\ costheta)

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RESONANCE DPP ENGLISH-JEE MAINS-All Questions
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