" 7."sin^(2)(2x+1)

5cos^(-1)((1-x^(2))/(1+x^(2)))+7sin^(-1)((2x)/(1+x^(2)))-4tan^(-1)((2x)/(1-x^(2)))-tan^(-1)x=5pi , then x is equal to

5cos^(-1)((1-x^(2))/(1+x^(2)))+7sin^(-1)((2x)/(1+x^(2)))-4tan^(-1)((2x)/(1-x^(2)))-tan^(-1)x=5pi , then x is equal to

int sin^(-(1)/(2))x cos^(-(7)/(2))xdx=

If sin x + sin ((pi)/(8) sqrt((1 - cos 2 x)^(2) + sin ^(2) 2 x)) = 0, x e [(5 pi)/(2), (7 pi)/(2)] , then x is

Prove that the value of each the following determinants is zero: sin^(2)(x+(3 pi)/(2))quad sin^(2)(x+(5 pi)/(2))quad sin^(2)(x+(7 pi)/(2))sin(x+(3 pi)/(2))quad sin(x+(5 pi)/(2))quad sin(x+(7 pi)/(2))sin(x-(3 pi)/(2))quad sin(x-(5 pi)/(2))quad sin(x-(7 pi)/(2))

The values of x in (0, pi) satisfying the equation. |{:(1+"sin"^(2)x, "sin"^(2)x, "sin"^(2)x), ("cos"^(2)x, 1+"cos"^(2)x, "cos"^(2)x), (4"sin" 2x, 4"sin"2x, 1+4"sin" 2x):}| = 0 , are

The values of x in (0, pi) satisfying the equation. |{:(1+"sin"^(2)x, "sin"^(2)x, "sin"^(2)x), ("cos"^(2)x, 1+"cos"^(2)x, "cos"^(2)x), (4"sin" 2x, 4"sin"2x, 1+4"sin" 2x):}| = 0 , are

int sin^(7)(3-2x)dx

"If " (tan x)/(tan y) = (1 + cos^(2) x)/(1 + sin^(2) x ) " show that "sin ( 3x + y) =7sin (x-y).