Question

Q:-If tan θ =12/5 ,then show that 5 cos θ + 12 sin θ = 13
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Answer 1

Answer:

$\sf \: The\: property \:is \:shown\: in \\ \tt \: a+b=b+a is the \\ \tt Commutative \:Property \\ \tt of Addition. \\ \tt 1) The commutative \:property \\ \tt of\: addition \:states\: that \:while \\ \tt adding\: any\: of \:the \:two \:numbers \\ \tt in\: any \:order\: that\: won't \:affect\: the \\ \tt \: final\: answer \:of \:the\: addition$

Answer 2

Step-by-step explanation:

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$\red{\bold{\underline{\underline{QUESTION:-}}}}$

Q:-If tan θ =12/5 ,then show that 5 cos θ + 12 sin θ = 13

$\huge\tt\underline\blue{Answer }$

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$⟹\bold{tan \theta = \frac{p}{b} = \frac{12}{5}}$

$⟹ \bold{{h}^{2} = {p}^{2} + {b}^{2}}$

$⟹\bold{ {h}^{2} = 144 + 125 = 169}$

$⟹\bold{h = \sqrt{169} = 13}$

$⟹\bold{cos \theta = \frac{b}{h} = \frac{5}{13}}$

$⟹\bold{sin \theta = \frac{p}{h} = \frac{12}{13} }$

$\bold{Now \: 5 \times \frac{5}{13} + 12 \times \frac{12}{13} = 13}$

$⟹\bold{ \frac{25}{13} + \frac{144}{13} = 13}$

$⟹\bold{ \frac{169}{13} = 13}$

$\bold{13 = 13}$

$\bold{\red{From\: above\: it\: is\: proved \:that [tex]tan\theta=12/5}}$

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