Q) If sec θ + tan θ = p, obtain the values of sec θ, tan θ and sin θ in terms of p.

Ans:  

sec θ + tan θ = p ………….. (i)

∵ sec² θ  – tan² θ = 1

∴ (sec θ + tan θ) (sec θ – tan θ) = 1

∴ p (sec θ – tan θ) = 1

∴ sec θ – tan θ = ………… (ii)

By adding equations (i) and (ii), we get:

2 sec θ = p + = 

∴ sec θ =

By subtracting equation (ii) from (i), we get:

2 tan θ = p – =

∴ tan θ =

∴ tan θ =

∴

∴ sin θ x sec θ =

∴ sin θ x =

∴ sin θ =

∴ sin θ =