Question

If x sin3|+ y cos3|=sin|cos| and xsin|=ycos|, prove x2+y2=1.

Answer 1

x sin^3 € + y cos ^3 € = sin € cos €

Since, Given, x sin€ = y cos €

x sin € ( sin^2 €) + y cos € ( cos^2 € ) = sin€ cos €

y cos € ( sin^2 € ) + y cos € ( cos^2 € = sin€ cos€

y cos€ ( sin^2 € + cos^2 €) = sin € cos €

Cos € will cancel out from both sides, and by identity, sin^2 € + cos^2 € = 1

y = sin € --> ( i )

x sin € = y cos €

x sin € = sin€ cos € [ y = sin € ]

x = cos € --> ( ii )

Squaring and adding equations ( i ) and ( ii ),

x^2 + y^2 = sin^2 € + cos^2 €

$\fbox{x^2\: +\: y^2\: = \:1.}$

Answer 2

If x sin3|+ y cos3|=sin|cos| and xsin|=ycos|, prove x2+y2=1.

Answer:

Answer:

Here is ur answer dear:-

=> xsin³theta + ycos³theta= sintheta×costheta.

=> x.sin³theta + cos²theta.(ycostheta) = sintheta.costheta.

• [use xsintheta= ycostheta in above]

=> xsin³theta+ cos²theta× xsintheta= sintheta×costheta.

=> xsintheta( sin²theta + cos²theta) = sintheta×costheta.

=> xsintheta = sintheta×costheta.

=> x = costheta.

=> s o, y = sintheta.