Question

if sinA.tanA÷cosA =9,prove that sinA =3÷√10

Answer 1

Answer:

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Answer 2

$\mathfrak{\large{\purple{SolutioN!}}}$

$\sf{\frac{sinA.tanA}{cosA} = 9}$

$\sf{{ \frac{sinA}{cosA} }.tanA = 9}$

$\sf{tanA.tanA = 9}$

$\sf{tan² A = 9}$

$\sf{\blue{Take\: square\: both\: sides,}}$

$\sf{tanA = ± 3}$

$\sf{Here\; ,we \:take\: tanA = 3 = \frac{3}{1} = \frac{p}{b} }$

$\sf{we\: know, sinA = \frac{p}{h} }$

$\sf{h = √(p² + b²) = √(3² + 1²) = √10}$

$\sf{\green{hence , sinA = \frac{p}{h} = \frac{3}{ \sqrt{10} } }}$

HOPE THIS HELPS YOU!!!