Question

If 8 tan x = 15, then cos x – sin x is equal to

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• 8TanX=15

${\sf{\green{\underline{\large{To\:find}}}}}$

• Cos X - Sin X

${\sf{\pink{\underline{\Large{Explanation}}}}}$

• we know that

$\tt{Tan}\theta=\frac{p}{b}$

$\tt{Tan}\theta=\frac{15}{8}$

Let the given tratios be k

Therefore

From Pythagoras Theorm

P²+b²=h²

¶utting value

=>(15)²+(8)²=h²

=>225k²+64k²=h²

=>h²=289k²

=>h=√289k²

=>h=17k

Now Finding Given values

Sin X = p/h = 15k/17k = 15/17

Cos X = b/h = 8k/17k = 8/17

Now Cos X -Sin X

$\tt\rightarrow\frac{8}{17}-\frac{15{17}$

$\tt\rightarrow\frac{8-15}{17}$

$\tt\rightarrow\frac{-7}{17}$

Hence value is -17/17

Answer 2

$\large\bf{ \red{ \underline{ \underline{Answer :}}}} \\ \\ \: \: \: \purple{ \frac{ - 7}{17} }$

• Gɪᴠᴇɴ

$\tt{8 \: Tan \;x = 15 \: - - - - - (1)}$

________________________________________

$\tt{ \implies Tan \: x = \frac{15}{8} } \\ \\ \bf \underline {Using \: Pythagorous \: Rule : } \\ \\ \tt{AC = \sqrt{ {8}^{2} + {15}^{2} }} \\ \\ \: \: \: \: \: \: \tt = \sqrt{64 + 225} \\ \\ \: \: \: \: \: \: \tt = \sqrt{289} = 17 \\ \\ \tt\therefore AC = 17 \\ \\ \tt{Now \: Sin \: x = \frac{15}{17} \: \: \: \: \: \: \: Cos \: x = \frac{8}{17} } \\ \\ \tt{ \implies Cos \: x - Sin \: x} \\ \\ \tt{ \implies \frac{8}{17} - \frac{15}{17} } \\ \\ \purple{ \implies \purple{\tt{ \underline {\boxed{ \frac{ - 17}{ 12} }}}}}$