Question

if cos theta =3/5 find the value of cot theta +cosec theta

Answer 1

Answer:

value of (cotθ + cosecθ) = 2

Step-by-step explanation:

given that:

cosθ = 3/5

we have to find the value of cotθ + cosecθ

cotθ can be written as cosθ/sinθ

cosecθ can be written as 1/sinθ

from formula, sin²θ = 1 - cos²θ

sin²θ = 1 - (3/5)²

= 1 - 9/25

=(25 - 9)/25 = 16/25 = (4/5)²

sin²θ = (4/5)²

sin θ = 4/5

so (cotθ + cosecθ) = cosθ/sinθ + 1/sinθ

= (cosθ + 1)/sinθ

substitute cosθ , sinθ values;

(cotθ + cosecθ) = [(3/5) + 1)]/(4/5)

= [(3 + 5)/5]/(4/5)

= (8/5)/(4/5)

= (8/4) = 2

value of (cotθ + cosecθ) = 2