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**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 + tan^{2} θ = sec^{2} θ

∴ tan^{2} θ – sec^{2} 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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