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

Step-by-step explanation:

tanθ=

b

p = 512⟹h2=p2+b2⟹ \bold{{h}^{2} = {p}^{2} + {b}^{2}}⟹h

2

=p

2

+b

2

⟹h2=144+125=169⟹\bold{ {h}^{2} = 144 + 125 = 169}⟹h

2

=144+125=169

⟹h=169=13⟹\bold{h = \sqrt{169} = 13}⟹h=

169

=13

⟹cosθ=bh=513⟹\bold{cos \theta = \frac{b}{h} = \frac{5}{13}}⟹cosθ=

h

b

=

13

5

⟹sinθ=ph=1213⟹\bold{sin \theta = \frac{p}{h} = \frac{12}{13} }⟹sinθ=

h

p

=

13

12

Now5×513+12×1213=13\bold{Now \: 5 \times \frac{5}{13} + 12 \times \frac{12}{13} = 13}Now5×

13

5

+12×

13

12

=13

⟹2513+14413=13⟹\bold{ \frac{25}{13} + \frac{144}{13} = 13}⟹

13

25

+

13

144

=13

⟹16913=13⟹\bold{ \frac{169}{13} = 13}⟹

13

169

=13

13=13\bold{13 = 13}13=13