24?????
Q1
x-y=1/3
and cos2(Ï€x)-sin2(Ï€y)=1/2
Find all solns (x,y)
Q2 cos(x-y)-2sinx-2siny=3 iff ??
Q3total integral values of n such that sinx(sinx+cosx)=n has atleast one soln
Q4 i=1Σn(sinθi+cosθi)≥n.√2
find i=1Σn(tanθi+cotθi)
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4 Answers
11Last one is easy....sin\theta_{i}+cos\theta_{i}=\pm\sqrt{1+sin2\theta_i}
Taking positive sign for the moment, we get sin2\theta_i=1 for all \theta_i......
Rest is easy.....
113)
sinx\sqrt{1+sin2x}=n.....which again gives R.H.S =L.H.S \le 2 ...thus
n=\left(0,\pm1,\pm 2 \right).
24whats ur ans in Q4 ???
and in Q3 u made a mistake
sinx ε [-1,1]
& 1+sin2x ε [0,2]
√1+sin2x ε [0,√2]
so sinx.√1+sin2x ε [1,√2]
=> n ε [1,√2]
=>n=0,1