Trigonometric EquationMedium
Question
If (sec A - tan A) (sec B - tan B). (sec C - tan C) = (sec A + tan A) (sec B + tan B) (sec C + tan C), then each side is equal to-
Options
A.0
B.1
C.-1
D.±1
Solution
(sec A - tan A) (sec B - tan B) (sec C - tan C)
= (sec A + tan A) (sec B + tan B) (sec C + tan C) = K
then (sec A - tan A)2 (sec B - tan B)2 (sec C - tan C)2 = 1
K2 = 1 ⇒ K = ± 1
= (sec A + tan A) (sec B + tan B) (sec C + tan C) = K
then (sec A - tan A)2 (sec B - tan B)2 (sec C - tan C)2 = 1
K2 = 1 ⇒ K = ± 1
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