Question

if xcosA=1 and ycotA=1,then the value of x^2-y^2 is​

Answer 1

Taking x and y values,

x\cos A=1xcosA=1

x=\frac{1}{\cos A}x=

cosA

1

x=\sec Ax=secA

and y=\tan Ay=tanA

Substitute in the expression,

x^2-y^2=(\sec A)^2-(\tan A)^2x

2

−y

2

=(secA)

2

−(tanA)

2

x^2-y^2=\sec^2 A-\tan^2 Ax

2

−y

2

=sec

2

A−tan

2

A

Using trigonometric identity, \sec^2 A-\tan^2 A=1sec

2

A−tan

2

A=1

So, x^2-y^2=1x

2

−y

2

=1