SSC CGL 2022 PYQ — Question 67

The correct answer is option 4 i.e. $\frac{{24}}{{5}}$

Given:

tanθ + secθ = 7

Concept used:

1. sec²θ - tan²θ = 1

2. tanα = sinα/cosα

3. secα = 1/cosα

Calculation:

tanθ + secθ = 7   ....(1)

We know,

sec²θ - tan²θ = 1

⇒ (secθ - tanθ) (secθ + tanθ) = 1

⇒ (secθ - tanθ) × 7 = 1          (From 1)

⇒ (secθ - tanθ) = 1/7   ...(2)

By adding (1) and (2) we get,

⇒ 2 secθ = 7 + 1/7 = 50/7

⇒ secθ = 25/7

By subtracting (1) and (2) we get,

⇒ 2 tanθ = 7 - 1/7 = 48/7

⇒ tanθ = 24/7

secθ = 25/7 and tanθ= 24/7

So, sinθ

⇒ tanθ / secθ

⇒ 24/7 / 25 / 7

⇒ 24/25

Now, 5sinθ

⇒ 5sinθ = 5 × 24 / 25 = 24/5

:. The value of 5 sinθ is 24/5