The value of 1 sin4 90o minus theta 1 cos2 90o minus theta minus 1 is ........

Quantitative Aptitude ( CCS) Trignometry

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The value of (1/sin⁴(90^o−θ)) + (1 /(cos²(90^o−θ)−1) is,

tan⁴θ

tan²θsec²θ

sec⁴θ

tan²θsin²θ

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Explanation:

Converting complementary angles first, we get the target expression E as,
E=1/sin⁴(900−θ)+1/(cos²(900−θ)−1)
=1/cos⁴θ+1/(sin²θ−1).
Then it is straightforward trigonometric simplification,
E=1/cos⁴θ−1/cos²θ, coverting 1−sin²θ to cos²θ,
=1(sec²θ−1)/cos²θ
=tan²θsec²θ.