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}

\frac{9}{1}

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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Sine, Cosine And Tangent Of An Angle

Trigonometry

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