If △ABC, if ∠B = 90º, AB = 21 cm and BC = 20 cm, then (1 + sin A - cos A)/(1 + sin A + cos A) is equal to:

If △ABC, if ∠B = 90º, AB = 21 cm and BC = 20 cm, then…

Comprehension:
In the following passage, some words have been deleted. Select the most appropriate option
to fill in each blank.
In the 19th century, there was an industrial revolution in Europe. As a result, millions of people
left the (1) ______ and went to work in big factories in cities. Today, it is the reverse. In several
major cities, people have started moving out. Why? They want a cleaner, (2) ______
environment. There are fewer jobs in ‘heavy’ industries like steel and power generation. (3)
______, there are more jobs in service industries like banking, tourism and food delivery.
Besides, modern transport and communications have made it easier for people to (4) ______
to work or even work from home. The result of this revolution in the 21st century will be
‘spread cities’ – cities are growing fast, but (5) ______, away from city centres and people are
choosing to live 40, 50 or 60 kilometres away.

If △ABC, if ∠B = 90º, AB = 21 cm and BC = 20 cm, then $\frac{{1 + \sin A - \cos A}}{{1 + \sin A + \cos A}}$ is equal to:

Show answer & explanation

Correct answer: C

Explanation

The correct answer in option 3 i.e. 2/5

AC² = 21² + 20² = 841

⇒ AC = 29 cm

sin A = P/H = $\frac{BC}{AC}$

⇒ sin A = 20/29

cos A = B/ H = $\frac{AB}{AC}$

⇒ cos A = 21/29

$\rm \frac{1 \space +\space sinA \space -\space cosA}{1 \space + \space sinA \space + \space cosA}$ = $\rm \frac{1 \space +\space \frac{20}{29}\space -\space \frac{21}{29}}{1 \space + \space \frac{20}{29} \space + \space \frac{21}{29}}$

⇒ $\rm \frac{\space \space \frac{29 + 20 -21}{29}}{ \space \space \space \frac{29 + 20 +21}{29}}$

⇒ $\frac{28}{70}$ = $\frac{2}{5}$

SSC CHSL 2021 PYQ — Question 67