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If sec^4(theta) - sec^2(theta) = 3, then the value of tan^4(theta) + tan^2(theta) is:
A8
B3
C4
D6
Answer & Solution
Correct answer: B. 3
1. Let s = sec^2(theta) = 1 + tan^2(theta). Then s^2 - s = s(s - 1) = 3.
2. Here s - 1 = tan^2(theta), so s(s-1) = (1 + tan^2)(tan^2) = tan^2 + tan^4.
3. Thus tan^4(theta) + tan^2(theta) = 3.
_Source: RRB Group D CEN-02/2018 PYQ, Q.57._
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