UPSC NDA Math Model Paper 8

Given: tan θ + sec θ = 4
To Find: sin θ
tan θ + sec θ = 4 .... (1)
As we know sec2θ−tan2θ=1
⇒ (sec θ + tan θ) × (sec θ - tan θ) = 1
⇒ 4 × (sec θ - tan θ) = 1
∴sec‌θ−tan‌θ=

1

4

.... (2)
Adding equation (1) + (2), we get
⇒2‌sec‌θ=4+

1

4

⇒sec‌θ=

17

8

⇒cos‌θ=

8

17

Now,
sin‌θ=√1−cos2θ
=√1−(

8

17

)2=

15

17