Q6 of 45 Page 1

Write the principal value of cot^-1 (-√3).

To find: the principal value of cot^-1 (-√3)

Let y = cot^-1 (-√3)

⇒ cot y = -√3

We know,

cot 30° = √3

{∵ cot θ = x ⇒ cot (π - θ) = -x}

cot y = -√3

The range of principal value of cot^-1 is (0, π)

Hence, the principal value of cot^-1 (-√3) is

If the length of three sides of a trapezium other than the base is 10 cm each, find the area of the trapezium, when it is maximum.

Find the intervals in which the following function is :

(a) strictly increasing

(b)strictly decreasing

f(x) = sinx + cosx, 0 ≤ x ≤ 2π

If and vector b are two vectors such that | vector a vector b| = | vector a x vector b| then what is the angle between and ?

Prove the following:

Solve for x :

Write the principal value of cot-1 (-√3).