Question

$\footnotesize \sf \red{If \: 3SinA=4CosA, \: find \: 4Sin²A \: − \: 3Cos²A+2} \: \large \bf \red{ \: \: =} \huge\sf \red{ \: \: ?}\ \textless \ br /\ \textgreater \ ​$
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Answer 1

${\pmb{\underline{\sf{Required \: Solution \: !!! }}}}$

${\bold{\green{\underline{\underline{Given}}}}}:3 \sin A= 4 \cos \: A$

We can write it as ;

$\boxed{\frac{ \sin A }{ \cos A } = \frac{4}{3} }$

$: \implies \tan A = \frac{4}{3} \: \: ( \frac{p}{b} )$

Find Hypotenuse :-

☆ For Diagram refer to the Attachment!!

Pythagoras Theorem

➠ H = √ P² + B²

H = √4² + 3²

H = √ 16 + 9

H = √25

$\boxed{H = 5}$

So, According to Question ;

$\implies 4 \: Sin\: {}^{2} A - 3 \: Cos \: {}^{2} A + 2 \\ \\ \implies 4 \times ( \frac{4}{5} ) {}^{2} - 3 \times (\frac{3}{5}) ^{2}+2 \\ \\ \implies 4 \times \frac{16}{25} - 3 \times \frac{9}{25} +2 \\ \\ \implies \frac{64}{25} - \frac{27} {25} + 2 \\ \\ \implies \frac{64-27}{25} + 2 \\ \\ \implies \frac{37}{25} +2 \\ \\ \implies\frac{37+50}{25} \\ \\ :\implies \boxed{\frac{87}{25}}$

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$\sf\blue{hope \: this \: helps \: you!! \: }$

@Mahor2111

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Answer 2

Answer:

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