SSC CHSL 2024 PYQ — Question 60

The correct answer is option 1 i.e. 3.

cot A = $\frac{cos A}{sinA}$= 7

cos A = 7sin A

$\frac{5cosA+4sinA}{cos^3A+7sin^3A+6sinA}$

Since cos⁡ A = 7sin ⁡A, we can put this into the expression:

(5(7sin A) + 4sin A)/ ((7sin A)$^3$ + 7sin$^3$ A + 6sin A)

$\frac{39sinA}{350 sin^3A + 6 sinA}$ = $\frac{39}{350 sin^2A +6}$

According to the identity sin$^2$ A + cos$^2$ A = 1

sin$^2$ A + (7sin A)$^2$ = 1                               (cos A = 7sin A)

⟹ sin$^2$ A(1 + 49) = 1

⟹ sin$^2$ A = 1/50

Hence

$\frac{39}{350×\frac{1}{50} +6}$ = $\frac{39}{7+6}$= $\frac{39}{13}$ = 3