If [Image] =5, then the value of [Image] is :

In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank.
John was an artist (1)______ profession. He was very (2)______ at his work and could
(3)______ any subject he could think of, but circumstances forced him to (4)______ in
(5)______ the work of renowned artists.

If =5, then the value of is :

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. $\frac{75}{34}$

(sinθ + cosθ)/(sinθ - cosθ) = 5

(sinθ + cosθ + sinθ - cosθ)/(sinθ + cosθ - sinθ + cosθ) = (5 + 1)/(5 - 1)

2sinθ/2cosθ) = 6/4

tanθ = perpendicular/base = 3/2

hypotenuse² = perpendicular² + base² = 3²+ 2² = 13

hypotenuse = √13

(4sin²θ + 3)/(2cos²θ + 2) = [4(3/√13)² + 3]/[2(2/√13)² + 2] = [4(9/13) + 3]/[2(4/13) + 2] = (36 + 39)/(8 + 26) = 75/34

SSC CGL 2021 PYQ — Question 71