Question

The set values of x for which the equation

cos^–1 x + cos^–1$\left( \frac{x}{2} + \frac{1}{2}\sqrt{3 - 3x^{2}} \right)$=$\frac{\pi}{3}$holds good, is –

• A. [0, 1]
• B. $\left\lbrack 0,\frac{1}{2} \right\rbrack$
• C. $\left\lbrack \frac{1}{2},1 \right\rbrack$
• D. {–1, 0, 1}

Answer 1

Answer: (C)

$\left\lbrack \frac{1}{2},1 \right\rbrack$

Answer 2

k = cos–1 x + cos–1 $\left\lbrack \frac{x}{2} + \frac{1}{2}\sqrt{3 - 3x^{2}} \right\rbrack$=$\frac{\pi}{3}$

\ –1 £ x £ 1, also 3 – 3x2 ³ 0

–1 £ $\frac{x}{2}$+ $\frac { 1 } { 2 }$ $\sqrt{3 - 3x^{2}}$£ 1

̃ – 1 £ x £ 1

0 £ $\frac{x}{2}$+ 1 + $\frac { 1 } { 2 }$ $\sqrt{3–3x^{2}}$ £ 1 ...(2)

Solving (2) we get option (3)