Question

if sin x = 1/3, find cos x.cosec x + tan x.sec x

Answer 1

sin X= opposite/hypotenuse=1/3
adjacent=2√2
cos X.cosec X=cot X
cot X=2√2
tan X=1/2√2
sec X=3/2√2
ans= 2√2+√2=√2(2+1)

Answer 2

Given that sin x =1/3=opp/hyp

So by Pythagoras theorem we can find out adj length.
 
∴ adj=√8 
 from that,
cos x=adj/hyp=√8/3
cosec x=hyp/opp=3/1
tan x=opp/adj=1/√8
sec x=hyp/adj=3/√8
 
cos x.cosec x+tan x.sec x
=√8/3 x 3 +1/√8 x 3/√8
=√8+3/8
but √8=√4x2=2√2
∴ 2√2+3/8

∴  16√2+3/8