Question

If sinø= 1/3 , show that cosø cosec ø+tanø sec ø =16√2/8

Answer 1

Sin ∅=1/3.....(Given)

therefore, cosec∅=1/ sin∅

cosec ∅=3..... (1)

Sin²∅+Cos²∅=1

(1/3) ²+Cos²∅=1

1/9+Cos²∅=1

Cos²∅=1-1/9

Cos ²∅=8/9

Cos∅=√8/3.....(2)

Therefore, sec ∅=1/cos∅

sec∅=3/√8...... (3)

Now tan∅=Sin∅/Cos∅

tan∅=1/3/√8/3

tan∅=1/√8..... (3)

To show:cos∅×cosec∅+tan∅×sec∅=

16√2/8

Therefore, L. H. S=√8/3×3+1/√8×3/√8

=16√2/8=R.HS