Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

Simplify (cosx+sinx)/cosx - (sinx-cosx)/sinx = ?

Options
A 1 sec x csc x
B sec x csc x
Correct Answer
C 2 + sec x csc x
D 2 - sec x csc x
Correct Answer

Option B is the correct answer.

Detailed Explanation

(cosx+sinx)/cosx = 1 + tanx, (sinx-cosx)/sinx = 1 - cotx. So expression = (1+tanx) - (1-cotx) = tanx + cotx = sinx/cosx + cosx/sinx = (sin²x+cos²x)/(sinx cosx) = 1/(sinx cosx) = cscx secx.

Hint

Simplify each fraction separately and combine.

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 494 of 696
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