Question

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

$\huge{\bold☘}\mathfrak\pink{\bold{\underline{{ ℘ɧεŋσɱεŋศɭ}}}}{\bold☘}$

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

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

$\huge\orange{\overbrace{\red{\underbrace\color{blue}{\underbrace\color{black}{\colorbox{lime}{{\red\:{「Answer」}}}}}}}}$

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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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Answer 2

Answer:

tan θ = 12/5 .

5Cos θ +12 sin θ = 13

by using pythagorus property

we find hypotenuse

that is 13

then ,

5× 5/13 +12×12/13=13

25/13+144/13=13

25+144/13=13

169/13=13

13=13

hence proved