trino dbts

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=1Î£ⁿ(sinÎ¸_i+cosÎ¸_i)â‰¥n.√2
find _i=1Î£ⁿ(tanÎ¸_i+cotÎ¸_i)

4 Answers

?????

Last 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.....

3)
sinx\sqrt{1+sin2x}=n.....which again gives R.H.S =L.H.S \le 2 ...thus
n=\left(0,\pm1,\pm 2 \right).

whats ur ans in Q4 ???

and in Q3 u made a mistake

sinx Îµ [-1,1]
& 1+sin2x Îµ [0,2]

√1+sin2x Îµ [0,√2]

so sinx.√1+sin2x Îµ [1,√2]

=> n Îµ [1,√2]

=>n=0,1

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