Q)  If tan θ + sec θ = m, then prove that sec θ = .

Ans:

We are given: tan θ + sec θ = m ………… (i)

Next, we calculate value of tan θ + sec θ

To do that, we multiply and divide (tan θ + sec θ) by (tan θ – sec θ)

Hence, (tan θ + sec θ) = m

=  = m

We know that 1 + tan² θ = sec² θ

∴ tan² θ  – sec² θ  = – 1

= m

= m

∴ tan θ  – sec θ  = …… (ii)

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

(tan θ  + sec θ)  – (tan θ  – sec θ)  = m  –

∴ 2 sec θ  = m  +

∴ sec θ  =

Hence Proved !

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