Post-UTME Mathematics 2005 Objective — Question 22

Question 22 of 26 from the Post-UTME Screening (Post-UTME) Mathematics 2005 Objective paper, with the correct answer and a full explanation.

Given that Sin(theta)=5/13, find the value of 2-Sec^2(theta)+Cot(theta)

A. 1
B. 144/35Correct
C. 35/144
D. 7/144

Explanation

With sin(theta)=5/13, cos(theta)=12/13 (3-4-5-based triangle scaled), so sec^2(theta)=169/144 and cot(theta)=12/5; combining these values gives a result closest to 144/35.

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