Question

if x is equal to 10 + sin a and Y is equal to tan a minus sin and then prove that x square minus y square is equal to 4 by x y​

Answer 1

$since \\ x {}^{2} - y {}^{2} = 4 \sqrt{xy} \\ (tan a + sin a) {}^{2} + (tan a - sin a) {}^{2} \\ = \tan {}^{2} a + \sin {}^{2} a + 2 \: tan \: a \times sin \: \: a \: + \tan {}^{2} a + \sin {}^{2} a - 2 \: tan \: a\times sin \: a \\ \binom{ \sin^{2} a}{ \cos {}^{2}a } + \sin {}^{2} + 2 \times \frac{ sina }{cosa} \times sina + \binom{ \sin {}^{2} a}{ \cos {}^{2} a} - 2 \times \frac{ sina }{cosa} \times sin \:a$

I hope you solve it !