If `sinx+cos e cx=2,` then `sin^n x+cos e c^n x` is equal to `2` (b) `2^n` (c) `2^(n-1)` (d) `2^(n-2)`

If tan x + cot x =2 , then sin^(2n)x + cos^(2n) x is equal to

If sinx+cosecx=2 , then, for all n in N , the value of: sin^nx+cosec^nx= (a) 2 (b) 2^n (c) 2^(n-1) (d) 2^(n-2)

If f(x)=(cos x+i sin x)(cos2x+i sin2x)(cos3x+i sin3x)......(cos nx+i sin n and f(1)=1, then f^(11) is equal to (a) (n(n+1))/(2) (b) {(n(n+1))/(2)}^(2)(C)-{(n(n+1))/(2)}^(2) (d) none of these

If cos^(-1)x-cos^(-1)y/2=alpha,t h e n4x^2-4x ycosalpha+y^2 is equal to 4 (b) 2sin^2alpha (c) -4sin^2alpha (d) 4sin^2alpha

If quad f(x)=(cos x+i sin x)(cos2x+i sin2x)(cos3x+i sin3x)cos nx+i sin nx and f(1)=1, then f(1) is equal to (n(n+1))/(2) (b) {(n(n+1))/(2)}^(2)(c)-{(n(n+1))/(2)}^(2) (d) none of these

If tan x=n tan y,n in R^(+), then the maximum value of sec^(2)(x-y) is equal to (a) ((n+1)^(2))/(2n) (b) ((n+1)^(2))/(n)( c) ((n+1)^(2))/(2) (d) ((n+1)^(2))/(4n)

If A(n) represents the area bounded by the curve y=n*ln x, where n in N and n>1 the x-axis and the lines x=1 and x=e , then the value of A(n)+nA(n-1) is equal to a.(n^(2))/(e+1) b.(n^(2))/(e-1) c.n^(2) d.en ^(2)

If (lim)_(x->0)(sin(n x)[(a-n)n x-t a n x])/(x^2)=n (n >0) then the value of ' a ' is equal to 1/n b. n^2+1 c. (n^2+1)/n d. none