Question

Tan theta is 12/5 find 1+sin theta/ 1-sin theta

Answer 1

Given,

The value of tanθ = 12/5

To Find,

The value of (1+sinθ)/(1-sinθ)

Solution,

Since the value of tanθ is given to us

So,

tanθ = 12/5 = Perpendicular/Base

Now, by using the Pythagoras theorem

Hypotenuse = √(12²+5²) = 13

Now,

sinθ = Perpendicular/Hypotenuse = 12/13

So,

(1+sinθ)/(1-sinθ) = (1+12/13)/(1-12/13)

                         = (25/13)/(1/13)

                         = 25

Hence, the value of (1+sinθ)/(1-sinθ) = 25.

Answer 2

A theorem in geometry: the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

$tan\theta =\frac{perpendicular}{base}=\frac{12}{5}$

$AC^2=(AB)^2+(BC)^2$

$=(12)^2+(5)^2$

$=144+25$

$=169$

$AC=13$

$\frac{1+sin\theta}{1-sin\theta }$

where $sin\theta=\frac{12}{13}$

$\frac{1+\frac{12}{13} }{1-\frac{12}{13} } =\frac{\frac{13+12}{13} }{\frac{13-12}{13} }$

$=\frac{\frac{25}{13} }{\frac{1}{13} } =\frac{25\times13}{13\times 1}$

$=25$