If `e^(itheta)=costheta+isintheta,` find the value of `|[1,e^(ipi//3),e^(ipi//4)],[e^(-ipi//3),1,e^(i2pi//3)],[e^(-ipi//4),e^(-i2pi//3),1]|`

If e^(itheta)=costheta+is intheta, find the value of |1e^(ipi//3)e^(ipi//4)e^(-ipi//3)1e^(i2pi//3)e^(-ipi//4)e^(-i2pi//3)1|

In triangle ABC, the value of |[e^(-i2A),e^(iC),e^(iB)],[e^(iC),e^(-i2B),e^(iA)],[e^(iB),e^(iA),e^(-i2C)]|

If A+B+C=pi and e^(itheta)=costheta+isintheta and z=|[e^(2iA), e^(-iC), e^(-iB)] , [e^(-iC), e^(2iB), e^(-iA)], [e^(-iB), e^(-iA), e^(2iC)]| , then

If A , B ,C are angles of a triangle, then the value of |[e^(2i A),e^(-i C),e^(-i B)],[e^(-i C),e^(2i B),e^(-i A)],[e^(-i B),e^(-i A),e^(2i C)]| is (a) 1 (b) -1 (c) -2 (d) -4

The value of int_(-pi//4)^(pi//4)(e^(x)sec^(2)x)/(e^(2x)-1)dx , is

Statement-1 : If e^(itheta)=cos theta +isintheta and the value of e^(iA).e^(iB).e^(iC) is equal to -1, where A,B,C are the angles of a triangle. and Statement -2 : In any triangleABC , A + B +C = 180^(@)

If 2sin^2theta=3\ costheta,\ w h e r e\ 0lt=thetalt=2pi, then find the value of thetadot

Function f(x)=sin(lnx)-"cos"(lnx) is (a)M.I. in [e^(2npipi/4),e^(2npi+(3pi)/4)] (b)M.D. In [e^(2npi+(3pi)/4),e^(2npi+(7pi)/4)] (c)M.D. in [e^(2npi(5pi)/4),e^(2npipi/4)] (d)M.I. in [e^(2npi+(3pi)/4),e^(2npi+(7pi)/4)]

The value of lim_(x->1)(2-x)^(tan((pix)/2)) is e^(-2/pi) (b) e^(1/pi) (c) e^(2/pi) (d) e^(-1/pi)

A man walks a distance of 3 units from the origin towards the North-East (N45^0E) direction.From there, he walks a distance of 4 units towards the North-West (N45^0W) direction to reach a point Pdot Then, the position of P in the Argand plane is (a) 3e^((ipi)/4)+4i (b) (3-4i)e^((ipi)/4) (4+3i)e^((ipi)/4) (d) (3+4i)e^((ipi)/4)