Question

(i) If 0 is an acute angle and cosec 0 = √5, find the value of cot 0 – cos 0.
(ii) If 0 is an acute angle and tan 0 = 8/15. find the value of sec 0 + cosec 0.​

Answer 1

Answer:

cos∅=2/√5,cot∅=2

cot∅-cos∅=2-2/√5

Step-by-step explanation:

sec∅=√289/15,cosec∅=√289/8

sec∅+cosec∅=23√289/120

Answer 2

Answer:

i) 1.11

ii) 3.26

Step-by-step explanation:

i) If 0 is an acute angle cosec 0 = Hypotenuse/Perpendicular = √5/1

cot0 = base/perpendicular

cos0 = base/hypotenuse

Using pythagoras theorem,

Hyp²= Perp² + base²

⇒ Base²= Hyp² - Perp²

⇒Base²= (√5)² - 1²

⇒Base²= 5 - 1

⇒Base²= 4

⇒Base = √4 = 2

cot0= 2/1 = 2

cos0= 2/√5

therefore,

cot0 - cos0 = 2- (2/√5) = [(2√5)-2]/√5 ≈ 1.11

ii) tan0= perp/base = 8/15

Using Pythagoras Theorem,

Hyp² = Perp² + Base²

= 8² + 15²

= 64 + 225

= 289

∴ Hyp = √289

= 17

sec0= hyp/base

= 17/15

cosec0= hyp/perp

= 17/8

sec0+ cosec0= (17/15) + (17/8)

= 391/120 ≈ 3.26