Find-ordered-pair-of-x-y-given-x-y-0-2pi-if-3-sin-x-cos-y-1-and-5-sin-2-x-cos-2-y-5-

Question Number 14752 by Tinkutara last updated on 04/Jun/17

Find ordered pair of (x, y) given x, y \in

[0, 2 π] if 3^{\sin x + \cos y} = 1 and

5^{\sin^{2} x + \cos^{2} y} = 5

Commented by Tinkutara last updated on 04/Jun/17

Answer given is total 8 ordered pairs

and there is no such pair as your

answer .

Commented by 1kanika# last updated on 04/Jun/17

Is ordered pair is (3 π / 4, 5 π / 4)

Commented by mrW1 last updated on 04/Jun/17

\frac{3 π}{4}, \frac{5 π}{4} i s a l s o r i g h t, b u t i s j u s t o n e s o l u t i o n .

Commented by 1kanika# last updated on 04/Jun/17

my ans . is right one .

Answered by mrW1 last updated on 04/Jun/17

\sin x + \cos y = 0 \dots (i)

\sin^{2} x + \cos^{2} y = 1 \dots (i i)

\sin x = - \cos y

{(- \cos y)}^{2} + {(\cos y)}^{2} = 1

\cos y = \pm \frac{\sqrt{2}}{2}

\Rightarrow y = \frac{π}{4}, \frac{7 π}{4} o r \frac{3 π}{4}, \frac{5 π}{4}

\sin x = \mp \frac{\sqrt{2}}{2}

\Rightarrow x = \frac{5 π}{4}, \frac{7 π}{4} o r \frac{π}{4}, \frac{3 π}{4}

\Rightarrow t o t a l l y t h e r e a r e 8 p a i r s (x, y) :

\frac{π}{4}, \frac{3 π}{4}

\frac{π}{4}, \frac{5 π}{4}

\frac{3 π}{4}, \frac{3 π}{4}

\frac{3 π}{4}, \frac{5 π}{4}

\frac{5 π}{4}, \frac{π}{4}

\frac{5 π}{4}, \frac{7 π}{4}

\frac{7 π}{4}, \frac{π}{4}

\frac{7 π}{4}, \frac{7 π}{4}

Commented by Tinkutara last updated on 04/Jun/17

Sorry, but answers given in my book

are entirely different :

(\frac{π}{6}, \frac{2 π}{3}), (\frac{π}{6}, \frac{4 π}{3}), (\frac{5 π}{6}, \frac{2 π}{3}), (\frac{5 π}{6}, \frac{4 π}{3}),

(\frac{7 π}{6}, \frac{π}{3}), (\frac{7 π}{6}, \frac{5 π}{3}), (\frac{11 π}{6}, \frac{π}{3}), (\frac{11 π}{6}, \frac{5 π}{3}) .

Commented by ajfour last updated on 04/Jun/17

w r o n g a n s w e r s, w h a t b o o k ?

Commented by Tinkutara last updated on 04/Jun/17

{It}^{'} s my coaching {institute}^{'} s book for

JEE preparation in Class XI .

Commented by mrW1 last updated on 04/Jun/17

T h a t b o o k i s m i s l e a d i n g .

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