MCQ practice · SSC General Mathematics Board questions · Chapter 9: Trigonometric Ratio
(1 + cot²A)/(1 − cos²A) = which of the following?
Think it through first, then pick an option.
- a cosec⁴A
- b sin⁴A
- c cot⁴A
- d cos⁴A
Answer and explanation
Correct answer: a cosec⁴A
The numerator is cosec²A and the denominator is sin²A; the quotient is cosec²A · cosec²A = cosec⁴A.
Why the other options are wrong
- b sin⁴A: sin⁴A would be the inverted expression; here the numerator is cosec²A and the denominator sin²A.
- c cot⁴A: cot⁴A would need cot²A in the denominator; the denominator is 1 − cos²A = sin²A.
- d cos⁴A: It is not cos⁴A, because the numerator 1 + cot²A is cosec²A, not cos²A.
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