(i) Choose the correct answer from the Bracket. If cos^-1x = y, then y is equal to (a) π ≤ y ≤ π (b) 0 ≤ y ≤ π ​ (c) −π/2 ≤ y ≤ π/2

Question

(i) Choose the correct answer from the Bracket.

If cos^-1x = y, then y is equal to

(a) π ≤ y ≤ π

(b) 0 ≤ y ≤ π

(c) −\(\frac{π}{2} ≤ y ≤ \frac{π}{2}\) 

(d) 0 ≤ y ≤ π

(ii) Find the value of cos^-1 cos(\(\frac{7π}{3}\))

(iii) Solve for x if, tan^-1(\(\frac{1+x}{1-x}\)) = 2 tan^-1x

Answer 1

(i) Range of cos^-1x is [0, π] ⇒ 0 ≤ y ≤ π

(ii) Here (\(\frac{7π}{3}\)) lie outside the interval [0, π]. TO make it in the interval proceed as follows.

(iii)