Find the value of sec θ + cosec θ.

If θ is an acute angle and tan = 8/15, find the value of sec θ + cosec θ.

Answer :

Given tan θ = 8/15

θ is an acute angle

in the figure triangle OMP is a right angled triangle,

∠M = 90^o and ∠Q = θ

tanθ = PM/OL = 8/15

PM = 8, OM = 15

But OP² = OM² + PM² using Pythagoras theorem,

= 15² + 8²

= 225 + 64

= 289

= 17²

OP = 17

sec θ = OP/OM = 17/15

cosec θ = OP/PM = 17/8

Now,

sec θ + cosec θ = (17/15) + (17/8)

= (136 + 255)/120

= 391/120

= 3 (31/120)

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