Trigonometry> Find the value of acute angle A when, cos...

Find the value of acute angle A when, cos 2A = cos 60°×cos 30°

Rahul , 8 Years ago

Grade 10

1 Answers

Jitender singh

cos 2A = cos 60°×cos 30°

$=\frac{1}{2}\times\frac{\sqrt{3}}{2}$

$=\frac{1}{2}\times\frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{4}$ $=\frac{1}{2}\times\frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{4} \implies 2A=cos^{-1}(\frac{\sqrt{3}}{4})$ $=\frac{1}{2}\times\frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{4} \implies 2A=cos^{-1}(\frac{\sqrt{3}}{4}) \implies A=\frac{1}{2} cos^{-1}(\frac{\sqrt{3}}{4})$

and A $=\frac{1}{2}\times\frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{4} \implies 2A=cos^{-1}(\frac{\sqrt{3}}{4}) \implies A=\frac{1}{2} cos^{-1}(\frac{\sqrt{3}}{4}) A= \frac{64.34^{\circ}}{2}=32.17^{\circ}$ $=\frac{1}{2}\times\frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{4} \implies 2A=cos^{-1}(\frac{\sqrt{3}}{4}) \implies A=\frac{1}{2} cos^{-1}(\frac{\sqrt{3}}{4}) A= \frac{64.34^{\circ}}{2}=32.17^{\circ}$ = $=\frac{1}{2}\times\frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{4} \implies 2A=cos^{-1}(\frac{\sqrt{3}}{4}) \implies A=\frac{1}{2} cos^{-1}(\frac{\sqrt{3}}{4}) cos^{-1}(\frac{\sqrt{3}}{4})= 64.34^{\circ}$

So the concept is of inverse trigonometric .It is so simple ,there is one thing in this question which generally not being asked in exam is the values of cos other than 0, 30,45,60,90

Last Activity: 8 Years ago