If sec θ + tan θ = p, prove that

(i)

(ii)

(iii)

(i) Given: sec θ + tan θ = p ……(1)

Then, (sec θ + tan θ) × = p

⇒ = p

⇒ = p

⇒ sec θ – tan θ = (1/p) ……(2)

Adding equation (1) and (2), we get:

2 sec θ = p + (1/p)

⇒ sec θ =

Therefore, sec θ =

(ii) Given: sec θ + tan θ = p ……(1)

Then, (sec θ + tan θ) × = p

⇒ = p

⇒ = p

⇒ sec θ – tan θ = (1/p) ……(2)

Subtracting equation (2) from (1), we get:

2tan θ = p – (1/p)

⇒ tan θ =

(iii) Since sin θ = tan θ/sec θ

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