Question

if tan thita =8/15,find cos thita and cos(90-thita)

Answer 1

Answer:

Given tan θ = 8/15

θ is an acute angle

in the figure triangle OMP is a right angled triangle,

∠M=90

0

and ∠Q=θ

tanθ=PM/OL=8/15

Therefore, PM = 8, OM = 15

But OP

2

=OM

2

+PM

2

using Pythagoras theorem,

=15

2

+8

2

= 225 + 64

= 289

=17

2

Therefore, OP = 17

secθ=OP/OM

= 17/15

cosecθ=OP/PM

= 17/8

Now,

secθ+cosecθ = (17/15) + (17/8)

= (136 + 255)/ 120

= 391/120