Question

If the period of cos(cos x) + cos(sin x)is
k
then k =

Answer 1

SOLUTION ::

Let f(x) = cos(cos x) + cos(sin x)

Then

f[(π/2) +x]

= cos[cos{(π/2) +x} ] + cos[sin{(π/2) +x} ]

= cos(-sinx) + cos(cosx)

= cos(cos x) + cos(sin x) [ cosine is an even function]

= f(x)

So the period of cos(cos x) + cos(sin x) is π/2

So k = π/2

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Answer 2

Let f(x) = cos(cos x) + cos(sin x)

Then

f[(π/2) +x]

= cos[cos{(π/2) +x} ] + cos[sin{(π/2) +x} ]

= cos(-sinx) + cos(cosx)

= cos(cos x) + cos(sin x) [ cosine is an even function]

= f(x)

So the period of cos(cos x) + cos(sin x) is π/2

So k = π/2