Question

please solve it fast​

Answer 1

Answer:

hope it will help you

jai hind

Answer 2

$Given \: tan \theta + sin \theta = m \: --(1)$

$and \: tan \theta - sin \theta = n \: --(2)$

$\red{i ) mn}$

$= ( tan \theta + sin \theta)(tan \theta - sin \theta)$

$= tan^{2} \theta - sin^{2} \theta$

/* By algebraic identity */

$\boxed{ \pink{ (x+y)(x-y) = x^{2} - y^{2} }}$

$= \frac{sin^{2} \theta }{cos^{2} \theta } - sin^{2} \theta$

$= sin^{2} \theta [ \frac{1}{cos^{2} \theta } - 1 ]$

$= sin^{2} \theta ( sec^{2} \theta - 1 )$

$= sin^{2} \theta tan^{2} \theta \: --(3)$

$\red{ii) m^{2} - n^{2} }$

$= (tan \theta + sin \theta)^{2} - (tan \theta - sin \theta)^{2}$

$= 4 tan \theta sin \theta$

$\boxed{ \blue{ \because (x+y)^{2} - (x-y)^{2} = 4xy }}$

$= 4\sqrt{ tan^{2} \theta sin^{2} \theta }$

$= 4\sqrt{mn} \: \green { [ From \: (3) ]}$

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