If sec A = 5/4, verify that .

sec A=

We know sec θ =

⟹ Hypotenuse = 5 and base = 4

So, we construct a right triangle ABC, right angled at B such that

∠BAC = θ, hypotenuse= AC = 5 and Base = AB = 4

By Pythagoras theorem,

AC² = AB² + BC²

⟹ (5)² = (4)² + BC²

⟹ 25 = 16 + BC²

⟹ BC²= 25-16

⟹ BC²= 9

⟹ BC=3

∴ sin A = and cos A =

tan A =

So,

Now,

Hence proved