SSC CGL 2023 PYQ — Question 75

The correct answer is option 4 i.e. $\frac{12}{13}$.

⇒ secA + tanA = 5                ------------------(1)

⇒ secA - tanA  = 1/5            ------------------(2)

Add equation 1 and equation 2

⇒ secA + tanA = 5 

⇒ secA - tanA  = 1/5 

⇒ 2sec A = 26/5

⇒ sec A = 13/5 = h/b

Hence

p = $\sqrt{h^2 - b^2}$

⇒ p = $\sqrt{13^2 - 5^2}$

⇒ p = $\sqrt{169 - 25}$

⇒ p = $\sqrt{144}$ = 12

And sin A = p/h = 12/13