If tan θ θ = 54 5 4 find sin2θ θ - cos2θ

Question 1 Report

If tan $θ$ = $\frac{5}{4}$ find sin2 $θ$ - cos2 $θ$

\frac{9}{41}

$\frac{5}{4}$

1

$\frac{9}{1}$

0

Answer Details

(tan

θ

=

\frac{o p p}{a d j}

)
|AB|2 = 52 + 42

\to

|AB|2 = 41

\to

AB =

\sqrt{41}

sin2

θ

- cos2

θ

\to

\frac{5^{2}}{\sqrt{41}}

- (

{\frac{4}{\sqrt{41}}}^{2}

) =

\frac{25}{41}

-

\frac{16}{41}

= (

\frac{9}{41}

)

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