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Asked by Vidushi412 | 31 Mar, 2019, 21:10: PM
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Numerator   Nr = | sin x | - |cos x| varies from -1 to +1
 
Nr = -1  ,  when x = nπ  ,  where n = 0, 1, 2......
 
Nr = +1 , when  x = n (π/2) , where n = 1,2,3,.........
 
when Nr reaches the extreme values -1 or +1, Denominator Dr = | sin x | + |cos x| = 1
 
Denominator function Dr varies from 1 to 1.5  .
Since sin x and cos x are complimentary function i.e when one of them reaches maximum 1 otherone will be at minimum 0,
their sum always start from 1 and maximum 1.5 occurs , when | sin x | and | cos x | both are equal , ie at x= (2n+1)(π/4), n=0,1,2,3...
when denominator reaches maximum 1.5, Numerator is zero.
 
Hence overall effect of the function is it varies from minimum value  -1 to maximum value +1,
mimimum occurs at x = nπ , n=0,1,2......
maximum occurs at x = (2n+1)(π/2) , n =0,1,2...
 
hence difference between sucessive minimum or maximum is π .  Hence period is π
Answered by Thiyagarajan K | 01 Apr, 2019, 10:29: AM

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