Given:
![\cos 15^{\circ}](https://tex.z-dn.net/?f=%5Ccos%2015%5E%7B%5Ccirc%7D)
To find:
The exact value of cos 15°.
Solution:
![$\cos 15^{\circ}=\cos\frac{ 30^{\circ}}{2}](https://tex.z-dn.net/?f=%24%5Ccos%2015%5E%7B%5Ccirc%7D%3D%5Ccos%5Cfrac%7B%2030%5E%7B%5Ccirc%7D%7D%7B2%7D)
Using half-angle identity:
![$\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos (x)}{2}}](https://tex.z-dn.net/?f=%24%5Ccos%20%5Cleft%28%5Cfrac%7Bx%7D%7B2%7D%5Cright%29%3D%5Csqrt%7B%5Cfrac%7B1%2B%5Ccos%20%28x%29%7D%7B2%7D%7D)
![$\cos \frac{30^{\circ}}{2}=\sqrt{\frac{1+\cos \left(30^{\circ}\right)}{2}}](https://tex.z-dn.net/?f=%24%5Ccos%20%5Cfrac%7B30%5E%7B%5Ccirc%7D%7D%7B2%7D%3D%5Csqrt%7B%5Cfrac%7B1%2B%5Ccos%20%5Cleft%2830%5E%7B%5Ccirc%7D%5Cright%29%7D%7B2%7D%7D)
Using the trigonometric identity: ![\cos \left(30^{\circ}\right)=\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Ccos%20%5Cleft%2830%5E%7B%5Ccirc%7D%5Cright%29%3D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
![$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}](https://tex.z-dn.net/?f=%24%3D%5Csqrt%7B%5Cfrac%7B1%2B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%7D%7B2%7D%7D)
Let us first solve the fraction in the numerator.
![$=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}](https://tex.z-dn.net/?f=%24%3D%5Csqrt%7B%5Cfrac%7B%5Cfrac%7B2%2B%5Csqrt%7B3%7D%7D%7B2%7D%7D%7B2%7D%7D)
Using fraction rule: ![\frac{\frac{a}{b} }{c}=\frac{a}{b \cdot c}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7Ba%7D%7Bb%7D%20%7D%7Bc%7D%3D%5Cfrac%7Ba%7D%7Bb%20%5Ccdot%20c%7D)
![$=\sqrt{\frac {2+\sqrt{3}}{4}}](https://tex.z-dn.net/?f=%24%3D%5Csqrt%7B%5Cfrac%20%7B2%2B%5Csqrt%7B3%7D%7D%7B4%7D%7D)
Apply radical rule: ![\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%3D%5Cfrac%7B%5Csqrt%5Bn%5D%7Ba%7D%7D%7B%5Csqrt%5Bn%5D%7Bb%7D%7D)
![$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B%5Csqrt%7B2%2B%5Csqrt%7B3%7D%7D%7D%7B%5Csqrt%7B4%7D%7D)
Using
:
![$=\frac{\sqrt{2+\sqrt{3}}}{2}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B%5Csqrt%7B2%2B%5Csqrt%7B3%7D%7D%7D%7B2%7D)
![$\cos 15^\circ=\frac{\sqrt{2+\sqrt{3}}}{2}](https://tex.z-dn.net/?f=%24%5Ccos%2015%5E%5Ccirc%3D%5Cfrac%7B%5Csqrt%7B2%2B%5Csqrt%7B3%7D%7D%7D%7B2%7D)
Answer:
I think (D)
Step-by-step explanation:
Answer:
B is true
Step-by-step explanation:
ratio of all corresponding sides are equal
Answer
Find out the how long will it take the submarine to descend to the ocean floor
To proof
Formula
![r = \frac{d}{t}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
where d = distance traveled (or descended),
r = rate of travel , t = time
As given
A submarine descends at a rate of 2.6 kilometers per hour. If the ocean floor is 6.24 kilometers below sea level .
put all the values in the above formula
![2.6 = \frac{6.24}{t}](https://tex.z-dn.net/?f=2.6%20%3D%20%5Cfrac%7B6.24%7D%7Bt%7D)
![t = \frac{6.24}{2.6}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B6.24%7D%7B2.6%7D)
t = 2.4 hour
it take 2.4 hours the submarine to descend to the ocean floor .
Hence proved
Answer:
This is true
Step-by-step explanation: