Question

if tantheeta = 4/3 , what is the value of sintheeta + costheeta/sintheeta -costheeta​

Answer 1

$\sf\large\underline{Given:}$

• $\rm{Tan\theta=\dfrac{4}{3}}$

$\sf\large\underline{To\: Find:}$

• $\rm{The\: value\:of\:\dfrac{sin\theta+cos\theta}{sin\theta-cos\theta}=?}$

$\sf\large\underline{Solution:}$

• [Given,In right angle triangle p=4 and b=3 according to given value to calculate h here:-]

$\sf\large\underline{Formula\:used:}$

$\rm\green{\implies h^2=p^2+b^2}$

• Putting the value here]

$\rm{\implies h^2=4^2+3^2}$

$\rm{\implies h^2=16+9}$

$\rm{\implies h^2=25}$

$\rm{\implies h=\sqrt{25}}$

$\rm\purple{\implies h=5}$

• Now calculate for the final answer]
• As we know that , sin theta=P/h
• Cos theta=b/h

$\rm{\implies Sin\theta=\dfrac{p}{h}=\dfrac{4}{5}}$

$\rm{\implies Cos\theta=\dfrac{b}{h}=\dfrac{3}{5}}$

$\rm{\implies \dfrac{sin\theta+cos\theta}{sin\theta-cos\theta}}$

$\rm{\implies \frac{4}{5}+\frac{3}{5}\div\frac{4}{5}-\frac{3}{5}}$

$\rm{\implies \frac{4+3}{5}\div\frac{4-3}{5}}$

$\rm{\implies \frac{7}{5}\div\frac{1}{5}}$

$\rm{\implies \frac{7}{5}\times\frac{5}{1}}$

$\rm\red{\implies \frac{7}{1}=7}$

Hence,

• The required answer is 7