Science (English Medium) Class 12 - CBSE Question Bank Solutions

`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`

If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt"cos" alpha) = "x",` the sinx is equal to ____________.

The value of cot `("cosec"^-1 5/3 + "tan"^-1 2/3)` is ____________.

`"sin" {2  "cos"^-1 ((-3)/5)}` is equal to ____________.

The domain of the function defind by f(x) `= "sin"^-1 sqrt("x" - 1)` is ____________.

The value of sin (2tan^-1 (0.75)) is equal to ____________.

The value of expression 2 `"sec"^-1  2 + "sin"^-1 (1/2)`

The value of the expression tan `(1/2  "cos"^-1 2/sqrt3)`

`"cot" ("cosec"^-1  5/3 + "tan"^-1  2/3) =` ____________.

`"cos" (2  "tan"^-1 1/7) - "sin" (4  "sin"^-1 1/3) =` ____________.

`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 = "tan"^-1 1/8 =` ____________.

If tan^-1 2x + tan^-1 3x = `pi/4,` then x is ____________.

If `"tan"^-1 (("x" - 1)/("x" + 2)) + "tan"^-1 (("x" + 1)/("x" + 2)) = pi/4,` then x is equal to ____________.

The value of cot^-1 9 + cosec^-1 `(sqrt41/4)` is given by ____________.

If A is a square matrix, then A – A’ is a ____________.

For any square matrix A, AA^T is a ____________.

If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.

If the matrix A `= [(5,2,"x"),("y",2,-3),(4, "t",-7)]` is a symmetric matrix, then find the value of x, y and t respectively.

If a matrix A is both symmetric and skew-symmetric, then ____________.

The matrix `[(0,5,-7),(-5,0,11),(7,-11,0)]` is ____________.