Question

ʜᴇʏᴀ!! ☺️

ϙ , 4
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ɪғ , 3 sɪɴ ᴛʜᴇᴛᴀ + 4 ᴄᴏs ᴛʜᴇᴛᴀ = 5

ᴛʜᴇɴ ᴘʀᴏᴠᴇ ᴛʜᴀᴛ , ᴛᴀɴ ᴛʜᴇᴛᴀ = 3 / 4
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ᴘʟᴇᴀsᴇ ɴᴏ sᴘᴀᴍ!!

ᴛʜᴀɴᴋ ʏᴏᴜ!! 

★ ᴅᴇᴠɪʟ ᴋɪɴɢ

Answer 1

Hey friend..!! here's your answer
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GIVEN :
$3 \sin(theta) + 4 \cos(theta) = 5 \: - - - - - (1)$
TO PROVE :
$\tan(theta) = \frac{3}{4}$
We need to find the value of sin theta and cos theta ,

==> $3 \sin(theta) + 4\cos(theta) = 5 \\ \\==> 4 \cos(theta) = 5 - 3 \sin(theta) \\ \\ squaring \: \: both \: \: side \: \\ \\==> 16 { \cos}^{2} theta = 25 + {9sin}^{2} theta - 30sin (theta) \\ \\==> 16(1 - {sin}^{2} theta) = 25 + {9sin}^{2} theta - 30 \sin(theta) \\ \\ ==> 16 - 16 {sin}^{2} theta = 25 + {9sin}^{2} theta - 30 \sin(theta) \\ \\==> 25 + {9sin}^{2} theta - 30 \sin(theta ) - 16 + 16 {sin}^{2} theta = 0 \\ \\==> 25 {sin}^{2} theta - 30 \sin(theta) + 9 = 0 \\ \\ ==> {(5sin \: theta)}^{2} - 2 \times 5 \sin(theta) \times 3 + {3}^{2} = 0 \\ \\==> {(5 sin \: theta - 3)}^{2} = 0 \\ \\ ==> 5sin \: theta \: - 3 = 0 \\ \\==> \sin(theta) = \frac{3}{5} - - - - - (2)$

Now , To find the value cos theta , Put the value of sin theta in equation 1

==> $3 (\frac{3}{5}) + 4cos \: theta \: = 5 \\ \\==> \frac{9}{5} + 4cos \: theta \: = 5 \\ \\==> \frac{9 + 20cos \: theta}{5} = 5 \\ \\==> 9 + 20 \cos(theta) = 25 \\ \\==> 20 \cos(theta) = 25 - 9 \\ \\ ==> 20 \cos(theta) = 16 \\ \\ ==> cos \: theta \: = \frac{4}{5} - - - - -(3)$

Now Divide equation 1 by 2

==> $\frac{ \sin(theta) }{ \cos(theta) } = \frac{ \frac{3}{5} }{ \frac{4}{5} } \\ \\==> \tan(theta) = \frac{3}{5} \times \frac{5}{4} \\ \\==> \tan(theta) = \frac{3}{4}$

HENCE PROVED

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# Hope its help

Answer 2

Hey friend..!! here's your answer
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hope this attachment will help you
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