Question

if sec thatha + tan thetha = p then tan thetha =​

Answer 1

Answer:

Step-by-step explanation:

If sec θ + tan θ = p, then tan θ is equal to

1) 2p/(p2 – 1)

2) (p2 – 1)/2p

3) (p2 + 1)/2p

4) 2p/(p2 + 1)

Answer: (2) (p2 – 1)/2p

Solution:

Given,

sec θ + tan θ = p….(i)

We know that,

sec2θ – tan2θ = 1

(sec θ + tan θ)(sec θ – tan θ) = 1

p(sec θ – tan θ) = 1

sec θ – tan θ = 1/p….(ii)

Subtracting (ii) from (i),

sec θ + tan θ – sec θ + tan θ = p – (1/p)

2 tan θ = (p2 – 1)/p

tan θ = (p2 – 1)/2p