sin^(2)theta+cos^(2)theta pi pi

The value of theta lying between theta = 0 and theta = pi//2 and satisfying the equation |(1+sin^(2)theta,cos^(2)theta,4sin4theta),(sin^(2)theta,1+cos^(2)theta,4sin4theta),(sin^(2)theta,cos^(2)theta,1+4sin4theta)|=0 are a) 3pi//24 b) 5pi//24 c) 11pi//24 d) pi//24

The number of values of x lying in [-pi,pi] and satisfying 2sin^(2)theta=cos2 theta and sin2 theta+2cos2 theta cos theta-1=0 is

If f(theta)=|(cos^(2)theta ,cos theta sin theta, -sin theta),(cos theta sin theta, sin^(2)theta,cos theta),(sin theta,-cos theta,0)| then, f((pi)/(6))+f((pi)/(3))+f((pi)/(2))+f((2pi)/(3))+f((5pi)/(6))+f(pi)+……+f((53pi)/(6)) is equal to

If f(theta)=|(cos^(2)theta ,cos theta sin theta, -sin theta),(cos theta sin theta, sin^(2)theta,cos theta),(sin theta,-cos theta,0)| then, f((pi)/(6))+f((pi)/(3))+f((pi)/(2))+f((2pi)/(3))+f((5pi)/(6))+f(pi)+……+f((53pi)/(6)) is equal to

underset(theta to pi//2)lim (1-sin^(2)theta)/(cos theta(pi//2-theta))=

Let the be an integrable function defined on [0,a] if I_(1)=int_(pi//2)^(pi//2) cos theta f(sin theta cos ^(2) theta)d theta and I_(2)=int_(0)^(pi//2)sin 2 theta f(sin theta cos ^(2) theta)d theta then

If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos theta sin theta , sin^(2) theta , cos theta ],[sin theta ,-cos theta , 0]] ,then f ( pi / 7) is

If f(theta)=|(cos^(2) theta, cos theta sin theta, -sin theta),(cos theta sin theta, sin^(2) theta, cos theta),(sin theta, -cos theta, 0)| then f((pi)/12)=

If f(theta)=|[cos^(2)theta,cos theta sin theta,-sin theta],[cos theta sin theta,sin^(2)theta,cos theta],[sin theta,-cos theta,0]| , then f((pi)/(12))

If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos theta sin theta , sin^(2) theta , cos theta ],[sin theta ,-cos theta , 0]] ,then f ( pi / 7) is