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)|`

What is the value of sin^6theta+cos^6theta+3sin^2thetacos^2theta-1 ?

Prove that sin^(6)theta+cos^(6)theta=1-3sin^(2)theta.cos^(2)theta.

What is the maximum value of sin3thetacos2theta+cos3thetasin2theta ?

The expression (sin 8thetacos theta-sin6 thetacos 3 theta)/(cos 2 thetacos theta-sin 3 thetasin 4 theta) is equals:-

(1+log_(2)(x-4))/(log_(sqrt(2))(sqrt(x+3)-sqrt(x-3)))=1

log_(2-sqrt(3))backslash(2+sqrt(3))=-1

Prove that log_(2)log_(2)log_(sqrt(3))81=1

(1+(1)/(2x))log_(10)3+log_(10)2=log_(10)(27-sqrt(3))

Which of the following statement(s) is/are true? (a) log _(10)2 lies between (1)/(4) and (1)/(3) (b) log_(csc(pi/6))(cos backslash(pi)/(3))=-1( c) e^(ln(ln3)) is smaller than 1(d)log_(10)1+(1)/(2)log_(10)3+log_(10)(2+sqrt(3))=log_(10)(1+sqrt(3)+(2+sqrt(3)))

The value of 6+log_((3)/(2))((1)/(3sqrt(2))sqrt(4-(1)/(3sqrt(2))sqrt(4-...))