Question 1210429
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1) Solve 2(√4x+5) - (√3x+1) = 6, where x is an integer.
2) Given that sinx = -3/5, where 180° ≤ x ≤ 270° and cos y = - 15/17 , where 90° ≤ y ≤ 180°. 
   find the value of tan(x-y).
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        I will solve here problem  (2),  ONLY.



<pre>
Since sin(x) = -3/5 in QIII, it implies  cos(x) = {{{-sqrt(1-sin^2(x))}}} = -4/5.


Since cos(y) = -15/17 in QII,  it implies  sin(y) = {{{sqrt(1-cos^2(y))}}} = 8/17.


Therefore  tan(x) = {{{sin(x)/cos(x)}}} = {{{((-3/5))/((-4/5))}}} = 3/4,

           tan(y) = {{{sin(y)/cos(y)}}} = {{{((8/17))/((-15/17))}}} = -8/15.


Now apply the formula for tan(x-y)

    tan(x-y) = {{{(tan(x)-tan(y))/(1+tan(x)*tan(y))}}}.


In the numerator, we have  

    tan(x) - tan(y) = {{{(3/4) - (-8/15)}}} = {{{3/4 + 8/15}}} = {{{(3*15)/60 + (8*4)/60}}} = {{{(3*15+8*4)/60}}} = {{{77/60}}}.


In the denominator, we have

    1 + tan(x)*tan(y) = {{{1 + (3/4)*(-8/15)}}} = {{{1 - 24/60 }}} = {{{36/60}}}.


Thus finally  tan(x-y) = {{{((77/60))/((36/60))}}} = {{{77/36}}}.


<U>ANSWER</U>.  tan(x-y) = {{{77/36}}}.
</pre>

Part (2) is completed.



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