Question

If Tanø =a/b Find the value of sinø+cosø/sinø-cosø

Answer 1

Answer:

$\frac{b+a}{b-a}$

Step-by-step explanation:

Tan θ = $\frac{perpendicular}{base}$ = $\frac{b}{a}$

So, Perpendicular = b, base = a

Finding hypotenuse by Pythagorean Theorem:

$c^2 = a^2+b^2$

=> So, hypotenuse = c

Sin θ = $\frac{perpendicular}{hypotenuse}= \frac{b}{c}$

Cos θ = $\frac{base}{hypotenuse}= \frac{a}{c}$

So, Now finding $\frac{sin\theta+cos\theta}{sin\theta-cos\theta}$

=> $\frac{b}{c} + \frac{a}{c}$ ÷ $\frac{b}{c} - \frac{a}{c}$

=> $\frac{b+a}{c}$ ÷ $\frac{b-a}{c}$

=> $\frac{b+a}{c} * \frac{c}{b-a}$

=> $\frac{b+a}{b-a}$