Question

find 'x' from the equation Sec(90+A)+x.SinATanA(90+A)=Cos(90+A)

Answer 1

sec(90+A)+x sin A tan(90+A)=cos(90+A)
-cosec A +x sinA(-cot A)=-sin A
x sin A (-cos A/sin A)=-sin A + cosec A
x(-cos A)=(1/sin A)-sin A
x (-cos A)=(1-sin square)/sin A
x=(sin square A-1)/sin A cos A

Answer 2

Answer:

$x=\frac{sin^2A-1}{sin A cos A}$

Step-by-step explanation:

To Find :  sec(90+A)+x sin A tan(90+A)=cos(90+A)

Solution :

$sec(90+A)+x sin A tan(90+A)=cos(90+A)$

Identity : $sec(90+A) = -cosec A\\ tan(90+A) = -cot A\\cos(90+A) = -sin A$

$-cosec A +x sinA(-cot A)=-sin A$

$x sin A (\frac{-cos A}{sin A})=-sin A + cosec A$

$x(-cos A)=\frac{1}{sin A}-sin A$

$x (-cos A)=\frac{1-sin^2A}{sin A}$

$x=\frac{sin^2A-1}{sin A cos A}$

Hence the value of x is $x=\frac{sin^2A-1}{sin A cos A}$