If tan theta frac 5 4 find sin2 theta - cos2 th... - JAMB Mathematics 2006 Question
If tan \(\theta\) = \(\frac{5}{4}\) find sin2\(\theta\) - cos2\(\theta\)
A
\(\frac{9}{41}\)
B
\(\frac{5}{4}\)
C
1
D
\(\frac{9}{1}\)
correct option: a
(tan (\theta) = (\frac{opp}{adj}))
|AB|2 = 52 + 42 (\to) |AB|2 = 41
(\to) AB = (\sqrt{41}) sin2(\theta) - cos2(\theta)
(\to) (\frac{5^2}{\sqrt{41}}) - ((\frac{4}{\sqrt{41}}^2)) = (\frac{25}{41}) - (\frac{16}{41})
= ((\frac{9}{41}))
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