SSC CGL 2024 PYQ — Question 57

The correct answer is option 2 i.e. 7 + tan²A + cot²A

(sin A + cosec A)² + (cos A + sec A)²

= (sin²A + 2sinA cosecA + cosec²A) + (cos²A + 2cosA secA + sec²A)

= (sin²A + 2sinA(1/sinA) + cosec²A) + (cos²A + 2cosA(1/cosA) + sec²A)

= (sin²A + 2 + cosec²A) + (cos²A + 2 + sec²A)

= (sin²A + cos²A) + 2 + 2 + cosec²A + sec²A

= 1 + 4 + cosec²A + sec²A   [∵ sin²A + cos²A = 1]

= 5 + cosec²A + sec²A

= 5 + (1 + cot²A) + (1 + tan²A)   [∵ sec²A = 1 + tan²A and cosec²A = 1 + cot²A]

= 5 + 1 + cot²A + 1 + tan²A

= 7 + tan²A + cot²A

Therefore, the required value is 7 + tan²A + cot²A.