If sin x = 1/2, then find the value of (sec4x + cosec4x) − (tan4x + cot4x).
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Correct answer: A
Explanation
The correct answer is option 1 i.e. 26/3.
sin x = 1/2
⇒ x = 30°
Now, (sec4x + cosec4x) − (tan4x + cot4x)
= (sec430° + cosec430°) − (tan430° + cot430°)
= [(2/√3)4 + (2)4] − [(1/√3)4 + (√3)4]
= (16/9 + 16) − (1/9 + 9)
= 160/9 − 82/9
= 26/3