Question

If cosec theta = √5 and is less than 90°, find the value of cot theta - cos theta.
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Answer 1

Answer:

cosec theta = √5/1

sin theta = 1/√5

cos theta = √ (√5)^2 - 1^2/√5 (USE PYTHOGOREAN THEOREM)

Hence cos theta = √5 - 1/√5 = √4/√5 = 2/√5

cot theta = costheta/sintheta = 2/√5 x √5/1 = 2

cos theta = 2/√5 (as calculated earlier)

find the difference,

2 - 2/√5 (take LCM)

= 2√5 - √5/√5 =

= √5 ( 2-1) / √5 (taking root 5 as common)

2 - 1 = 1

Answer : 1.