Given:
\[ \cos A = \frac{\sqrt{21}}{5} \]
\[ \sin A = \frac{2}{5} \]
What is the exact value of \(\cos 2A\)?
Answer (2)
cos α = 5 21 ; s in α = 5 2 cos 2 α = co s 2 α − s i n 2 α co s 2 α = ( 5 21 ) 2 = 25 21 s i n 2 α = ( 5 2 ) 2 = 25 4 cos 2 α = 25 21 − 25 4 = 25 17
The exact value of cos 2 A is 25 17 . This is calculated using the double angle formula cos 2 A = cos 2 A − sin 2 A with the given values of cos A and sin A .
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