Question

cosec - cot = 1/2 then 0 < teta < 90° cos is equal to a) 3/5 b) - 5/3 c) 5/3 d)-3/5​

Answer 1

Answer

OPTION A and D both .

Step-by-step explanation:

We know by trigonometry that :

coseccosec²x - cot²x = 1

= ( cosecx + cotx )( cosecx - cotx ) = 1 -----(0)

Given in the question cosecx-cotx = 1/2 -----(1)

Hence from (0) :-

( cosec x + cot x ) × 1/2 = 1

= cosec x + cot x = 2 ------(2)

Add 1 and 2 together :

2 cosec x = 2 + 1/2

⇒ 2 cosec x = 5/2

⇒ cosec x = 5/4

We know that by trigonometry :

sin x = 1/cosecx = 4/5

We know by trigonometry that :

sin²x + cos²x = 1

putting the values of sin x we get :

⇒ 16/25 + cos²x = 1

⇒ cos²x = 1 - 16/25

⇒ cos²x = ( 25 - 16 ) / 25

⇒ cos²x = 9/25

Take square root both sides .

⇒ cos x = ± 3/5

Note that cos x can be - 3/5 also .

Hence the correct OPTION is A as well as D .

Answer 2

Step-by-step explanation:

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