Question

If tan θ = 3/4 , find the values of sec θ and cos θ.

Answer 1

Alternate method:

tanθ = 3/4 … (i) [Given]

Consider ∆ABC, where ∠ABC 90° and ∠ACB = θ. 

tan θ = AB/BC … (ii) [By definition] 

∴ AB/BC = 3/4 … [From (i) and (ii)]

Let AB = 3k and BC 4k 

In ∆ABC,∠B = 90° 

∴ AB² + BC² = AC² …[Pythagoras theorem] 

∴ (3k) + (4k) = AC 

∴ 9k² + 16k² = AC² 

∴ AC² = 25k² 

∴ AC = 5k …[Taking square root of both sides]