Question
Download Solution PDFIf sec A + tan A = 3, then cos A is equal to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven :
Sec θ + tan θ = 3
Formula used :
Sec2 θ - tan2 θ = 1 or (sec θ - tan θ) × (Sec θ + tan θ) = 1
Calculations :
(sec θ - tan θ) (sec θ + tan θ) = 1
sec θ - tan θ = 1/3 ....(1)
sec θ + tan θ = 3 ....(2) (given)
Solving equ (1) and (2)
⇒ Sec θ = 10/6 = 5/3
⇒ cos θ = 3/5 (cos θ = (1/sec θ)
∴ The answer is 3/5.
Last updated on Jul 19, 2025
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