Find the fundamental period of the following functions :
(i)f (x) = 2 + 3cos (x – 2) (ii)f(x) = sin 3x + cos 2 x + | tanx |
(iii)f (x) = sin 
+ sin 
(iv)f(x)= cos 
x − sin 
x.
(v)f(x) = 
(vi) f(x) = 
(vii)f(x) = sec 3 x + cosec 3 x
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) 2 π (ii) 2 π (iii) 24 (iv) 70 π
(v) 2 π (vi) π /6 (vii) 2 π
Sol. (i) f(x) = 2 + 3 cos (x – 2) fundamental period = 2 π
(ii) f(x) = sin 3x + cos 2 x + |tan x| ⇒ period → 
, π , π
period of f(x) = L.C.M. 
= 2 π ⇒ for fundamental period
f(x + π ) = – sin x + cos 2 x + |tan x| ≠ f(x)
∴ Fundament period = 2 π
(iii) f(x) = sin 
+ sin 
⇒ period → 8, 6 ⇒ period of f(x) = L.C.M. (8, 6) = 24
Fundamental period = 24
(iv) f(x) = cos 
– 
⇒ period → 
, 7 π ⇒ period of f(x) = L.C.M. 
= 70 π
Fundament period = 70 π.
(v) f(x)= 
fundamental period = 2 π
(vi) f(x) = 
⇒ period of f(x) = L.C.M. 
= 
for fundamental period
f 
= 
= f(x) ∴ Fundament period = 
(vii) f(x) = sec 3 x + cosec 3 x ⇒ period → 2 π ⇒ 2 π ⇒ Fundamental period = L.C.M. (2 π , 2 π )
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