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\(\theta\)
\(\to\) \(\frac{5^2}{\sqrt{41}}\) - (\(\frac{4}{\sqrt{41}}^2\)) = \(\frac{25}{41}\) - \(\frac{16}{41}\)
= (\(\frac{9}{41}\))
|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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