Question

if cot theta =3/4 and π< theta<3π/4 then find the value of 4 cosec theta +5 cos theta​

Answer 1

Answer:

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Answer 2

Given that cot∅ = 3/4

As cot∅ is positive,∅ would lie in third quadrant

From,cosec²∅ - cot²∅=1

→cosec²∅=1 + cot²∅

→cosec²∅ = 1+(3/4)²

→cosec²∅ = 25/16

→cosec∅ = ±5/4

→cosec∅ = -5/4

Also,

sin∅ = -4/5

We know that,

cos∅ = sin∅cot∅

→cos∅ = (-4/5)(3/4)

→cos∅ = -3/5

Now,

4cosec∅ + 5cos∅

= 4(-5/4) + 5(-3/5)

= -5 -3

= -8