Question

If sin theta =3/5 .evaluate cosec theta-cot theta/ 2 cot theta

Answer 1

sin theta=3/5

sin is perpendicular /hypotenuse

P=3 and H=5

now, H^2=P^2+B^2 ( by Pythagoras)

B^2=√ H^2-P^2

= √5^2-3^2

=√ 25-9

=√16=4

now, cos theta is B/H=4/5

tan theta=P/B=3/4

cot theta=B/P=4/3

now cot theta we can write as 1/tan theta

cosec theta-1/tan theta/2cot theta

4/5-1/3

_______

2×4/3

4/5-4/3

_______

8/3

12-20/15

________

8/3

12-20/15× 3/8

3 and15 cancelled

12-20/5=1/8

-8/5×1/8=-1/5