Question

If tan theta 4/3 what is the value of sin theta+ cos theta/ sin theta- cos theta

Answer 1

Given: tan∅ = 4/3

• Perpendicular = 4
• Base = 3

→ H² = 4² + 3²

→ H² = 25

→ H = ±5

(Here taking value as + 5)

sin∅ = Perpendicular/Hypotenuse = 4/5

cos∅ = Base/Hypotenuse = 3/5

→ (sin∅ + cos∅)/(sin∅ - cos∅)

By substituting values we get,

→ (4/5 + 3/5)/(4/5 - 3/5)

→ 7/5 × 5

→ 7

Hence correct answer is 7.

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

$\tt{\rightarrow tan\theta = \dfrac{4}{3}}$

✔As we know that :-

$\tt{\rightarrow tan\theta = \dfrac{Perpendicular}{Base}}$

✔Here we get the values of perpendicular and base :-

Perpendicular = 4

Base = 3

✔Now we have to find Hypotenuse

✔Using Pythagoras theorem,

$\tt{\rightarrow H = \sqrt{P^{2} + B^{2}}}$

$\tt{\rightarrow H = \sqrt{4^{2} + 3^{2}}}$

$\tt{\rightarrow H = \sqrt{16+9}}$

$\tt{\rightarrow \sqrt{25}}$

Hypotenuse = 5

Now :-

$\tt{\rightarrow sin\theta = \dfrac{4}{5}}$

$\tt{\rightarrow cos\theta = \dfrac{3}{5}}$

✔Substitute the values :-

$\tt{\rightarrow\dfrac{sin\theta+cos\theta}{sin\theta-cos\theta}}$

= 4/5 + 3/5 ÷ 4/5 - 3/5

= (4 + 3/5) ÷ (4 - 3/5)

= (7/5) ÷ (1/5)

$\tt{\rightarrow\dfrac{7}{5}\times \dfrac{5}{1}}$

$\tt{\rightarrow tan\theta = \dfrac{7}{1}}$

= 7