If \(\cos θ = \frac 5 {13},\) then the value of tan2 θ + sec2 θ

1.	If \(\cos θ = \frac 5 {13},\) then the value of tan2 θ + sec2 θ is equal to:1. \(\frac {313}{25}\)2. \(\frac {323}{25}\)3. \(\frac {233}{25}\)4. \(\frac {303}{25}\)
Answer» Correct Answer - Option 1 : \(\frac {313}{25}\) Given: \(\cos θ = \frac 5 {13}\) Concept used: 1 + tan2 θ = sec2 θ cosθ = 1/secθ Calculations: ⇒ tan2 θ + sec2 θ ⇒ sec2 θ - 1 + sec2 θ ⇒ 2sec2 θ - 1 ⇒ secθ = 13/5 ⇒ (2 × 169)/25 - 1 ⇒ (338/25) - 1 ⇒ (338 - 25)/25 ⇒ 313/25 ∴ The value of tan2 θ + sec2 θ is 313/25.

If \(\cos θ = \frac 5 {13},\) then the value of tan2 θ + sec2 θ is equal to:1. \(\frac {313}{25}\)2. \(\frac {323}{25}\)3. \(\frac {233}{25}\)4. \(\frac {303}{25}\)

Answer» Correct Answer - Option 1 : \(\frac {313}{25}\)

Given:

\(\cos θ = \frac 5 {13}\)

Concept used:

1 + tan2 θ = sec2 θ

cosθ = 1/secθ

Calculations:

⇒ tan2 θ + sec2 θ

⇒ sec2 θ - 1 + sec2 θ

⇒ 2sec2 θ - 1

⇒ secθ = 13/5

⇒ (2 × 169)/25 - 1

⇒ (338/25) - 1

⇒ (338 - 25)/25

⇒ 313/25

∴ The value of tan2 θ + sec2 θ is 313/25.