23. If 5sin x= 3, then sec x + tan x /sec x - tan x is equal to
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Answer:
Here it states: sec x - tan x / sec x + tan x.
Is it sec x - (tan x / sec x) + tan x …(1)
OR
[(sec x - tan x) / sec x ]+ tan x …(2)
OR
[sec x - tan x] / [sec x + tan x] … (3)
Each of (1), (2) and (3) give different answers.
Let us see how.
5 sin x = 3, or sin x = 3/5. Hence cos x = 4/5, tan x = 3/4, sec x = 5/4.
(1) : sec x - (tan x / sec x) + tan x
= (5/4) - (3/4)/(5/4) + (3/4)
= (8/4)-(15/16) =(17/16). Answer
(2) : [(sec x - tan x) / sec x ]+ tan x
= [{(5/4)-(3/4)}/(5/4)] + 3/4
= (2/4)*(4/5) + (3/4)
= (2/5) + (3/4)
= (8/20)+(15/20)
= (23/20). Answer
(3) : [sec x - tan x] / [sec x + tan x]
= [(5/4)-(3/4)]/[(5/4)+(3/4)]
= (2/4)/(8/4)
= (2/4)*(4/8)
= (1/4). Answer
3rd answer is most relevant to your question.
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Hope it helped (◍•ᴗ•◍)(◕ᴗ◕✿)
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