Question
Download Solution PDFIf sec x – cos x = 4, then what will be the value of
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
sec x – cos x = 4
Concept Used:
Cos x =
Calculation:
Let cos x = m
⇒ sec x – cos x = 4
⇒
⇒
⇒ 1 - m2 = 4m
⇒ m2 + 4m -1 = 0
Finding roots of the above equation:
⇒ m =
⇒ m =
⇒ m =
Finding the value:
⇒
Putting the value of m in above equation:
⇒
⇒ √5 + 2 + √5 - 2 =
Hence, the value of
Shortcut Trick
We know, if x - 1/x = a then x + 1/x = √(a2 + 4)
Here, similarly sec x - 1/sec x = 4, then sec x + 1/sec x = √(42 + 4) = √20 = 2√5
Last updated on Jul 17, 2025
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