Question

If $cosp=\frac{1}{7}andcosQ=\frac{13}{14}$, where P and Q both are acute angles. Then, the value of P - Q is

• A. ${30}^o$
• B. ${60}^o$
• C. ${45}^o$
• D. ${75}^o$

Answer 1

Answer: (B)

${60}^o$

$cosP=\frac{1}{7}$

$sinP=\sqrt{1-co{s}^{2}P}$

$=\sqrt{1-\frac{1}{49}}$

$=\sqrt{\frac{48}{49}}$

$=\frac{4\sqrt{3}}{7}$ ( $sinP$ will be positive because $P$ is an acute angle )

$cosQ=\frac{13}{14}$

$sinQ=\sqrt{1-co{s}^{2}Q}$

$=\sqrt{1-\frac{169}{196}}$

$=\sqrt{\frac{27}{196}}$

$=\frac{3\sqrt{3}}{14}$

Now,

$cos(P-Q)=cosPcosQ+sinPsinQ$

$=\frac{1}{7}\times \frac{13}{14}+\frac{4\sqrt{3}}{7}\times \frac{3\sqrt{3}}{14}$

$=\frac{49}{98}$

$=\frac{1}{2}$

$\Rightarrow P-Q={60}^{\circ }$