Question

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

Answer 1

Hey Mate !

Step-by-step explanation:

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 €

Hope it helps u !

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