Evaluate the determinants in(i) `|costheta-sinthetasinthetacostheta|` (ii) `|x^2-x+1x-1x+1x+1|`

Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sinthetasinthetacostheta| |cos15^0sin15^0sin75^0cos75^0| (iv) |a+i b c+i d-c+i d a-i b|

Evalute the determinants in queations 1 and 2 : (i) [{:(costheta,-sintheta),(sintheta,costheta):}| (ii) |{:(x^(2),-x+1,x-1),(,x+1,x+1):}|

Prove that the determinant |[x, sintheta,costheta],[-sintheta,-x,1],[costheta,1,x]| is independent of theta

Evaluate: (i) |(5 ,4),(-2, 3)| (ii) |(sintheta,costheta),(-costheta,sintheta)| (iii) |(x-1, 1),(1,x^2+x+1)|

Prove that the determinant |{:(x,sintheta,costheta),(-sintheta,-x,1),(costheta,1,x):}| is independent of theta .

Prove that the determinate abs([x,sintheta,costheta],[-sintheta,-x,1],[costheta,1,x]) is independent of theta

Evalute the determinants in queations 1 and 2 : Find the values of x, if (i) |{:(2,4),(5,1):}|=|{:(2x,4),(6,x):}| (ii) |{:(2,3),(4,5):}|=|{:(x,3),(2x,5):}|

If x=(2sintheta)/(1+costheta+sintheta),t h e n(1-costheta+sintheta)/(1+sintheta) is equal to 1+x (b) 1-x (c) x (d) 1/x

Evaluate the following: (i) int sqrt(1+sin((1)/(2)x))dx (ii) int(x^(2))/(sqrt(1-x))dx