How do you simplify $(cos^2ysin(y+pi/2))/(sin^2ysin(pi/2-y)$ ?

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Answer 1 · 2016-09-30T18:40:34

$cot^2y.$

We know that $sin(A+B)=sinAcosB+sinBcosA$

Using the above formula, we expand,

$sin(y+pi/2)=sinycos(pi/2)+cosysin(pi/2)$ ,

$=0*siny+1*cosy=cosy$

Similarly, $sin (pi/2-y)=cosy.$

Hence, the exp. $=(cos^2y*cosy)/(sin^2y*cosy)$

$=cos^2y/sin^2y=cot^2y$ .

How do you simplify (cos^2ysin(y+pi/2))/(sin^2ysin(pi/2-y)(cos^2ysin(y+pi/2))/(sin^2ysin(pi/2-y)?