Question

The value of cos (2cos^–1x + sin^–1x) at x = $\frac{1}{6}$:

• A. $\frac{\sqrt{37}}{6}$
• B. $–\frac{\sqrt{35}}{6}$
• C. $\frac{\sqrt{35}}{6}$
• D. – $\frac{\sqrt{37}}{6}$

Answer 1

Answer: (B)

$–\frac{\sqrt{35}}{6}$

Answer 2

cos (2cos^–1 x + sin^–1 x)

= cos $\left( \frac { \pi } { 2 } + \cos ^ { - 1 } x \right)$= –sin (cos^–1 x)

= – sin(sin^–1 $\sqrt { 1 - x ^ { 2 } }$) = – $\sqrt{1 - x^{2}}$

= –$\sqrt{1 - \left( \frac{1}{6} \right)^{2}}$= –$\sqrt{\frac{35}{36}}$

= –$\frac{\sqrt{35}}{6}$.