Question

please somebody help me in this sum​

Answer 1

$\large\bf\underline{\green{Given:}}$

$\implies \sf \tan( \theta) = \frac{5}{12}$

$\large\bf\underline{\green{To \: \:Find :}}$

$\implies \sf \frac{ \cos \theta - \sin \theta }{ \cos \theta + \sin \theta }$

$\large\bf\underline{\green{Sollution :}}$

$\bf \: as \: we \: know \: that \: \tan( \theta) = \frac{p}{b} \\ \bf \: now .........\\ \\ \implies \bf \: (hypotenuse) ^{2} \: = \sf \: (perpendicular)^{2} + (base) ^{2} \\ \\ \implies \: \bf \: (hyputenuse) ^{2} = \sf \: (5) ^{2} + (12) ^{2} \\ \\ \implies \bf (hyputenuse) ^{2} = \: \sf \: 25 + 144 \\ \\ \implies \bf \: (hyputenuse) = 13$

Now , cos θ = B/h and sin θ = P/h

$\sf \implies \: \sf \frac{ \cos \theta - \sin \theta }{ \cos \theta + \sin \theta } \\ \\ \implies \sf \: \frac{ \frac{12}{13} - \frac{5}{13} }{ \frac{12}{13} + \frac{5}{13} } \\ \\ \implies \sf \frac{ \frac{7}{13} }{ \frac{17}{13} } \\ \\ \implies \bf \frac{7}{17}$

Hence the value of (cos θ - sin θ )/(cos θ + sin θ) = 7/17

Answer 2

Given ,

Tan(Φ) = 5/12 = P/B

By Pythagoras theorem ,

(h)² = (5)² + (12)²

(h)² = 25 + 144

h = √169

h = ± 13

Therefore ,

• Hypotenuse = 13 units
• Cos(Φ) = B/H = 12/13
• Sin(Φ) = P/H = 5/13

And

Cos(Φ) - Sin(Φ) ÷ Cos(Φ) - Sin(Φ) will be equal to

$\sf \rightarrow \frac{ \frac{12}{13} - \frac{5}{13} }{ \frac{12}{13} + \frac{5}{13} } \\ \\ \sf \rightarrow \frac{7}{17}$

$\sf \therefore \underline{The \: required \: value \: is \: \frac{7}{17} }$