Question

plz solve it, its urgent.........

nhi aata toh plz answer na karna
plz
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plz​

Answer 1

EXPLANATION.

$\sf \: \implies \: ( \sec \theta \: - \: \tan\theta) {}^{2} = \dfrac{1 - \sin( \theta) }{1 + \sin( \theta) } \\ \\ \sf \: \implies \: from \: LHS \: \\ \\ \sf \: \implies \: ( \frac{1}{ \cos( \theta) } - \frac{ \sin( \theta) }{ \cos( \theta) }) {}^{2} \\ \\ \sf \: \implies \: ( \frac{1 - \sin( \theta) }{ \cos( \theta) } ) {}^{2}$

$\sf \: \implies \: from \: RHS \: \\ \\ \sf \: \implies \: \frac{1 - \sin( \theta) }{1 + \sin( \theta) } \: \times \: \frac{1 - \sin( \theta) }{1 - \sin( \theta) } \\ \\ \sf \: \implies \: \frac{(1 - \sin \theta) {}^{2} }{1 - \sin {}^{2} ( \theta) } \\ \\ \sf \: \implies \: (\frac{(1 - \sin( \theta) }{ \cos( \theta) } ) {}^{2} = proof$

$\sf \: \implies \: (2) = \dfrac{ \sin(a) }{1 + \cos(a) } + \dfrac{1 + \cos(a) }{ \sin(a) } = 2 \csc(a) \\ \\ \sf \: \implies \: \frac{( \sin(a)) {}^{2} + (1 + \cos(a)) {}^{2} }{(1 + \cos \: (a)( \sin(a) ) } \\ \\ \sf \: \implies \: \frac{ \sin {}^{2} (a) + (1) {}^{2} + \cos {}^{2} (a) + 2 \cos(a) }{(1 + \cos(a) )( \sin(a) ) } \\ \\ \sf \: \implies \: \frac{2 + 2 \cos(a) }{(1 + \cos(a)) ( \sin(a)) } \\ \\ \sf \: \implies \: \frac{2(1 + \cos(a)) }{(1 + \cos(a))( \sin(a)) } \\ \\ \sf \: \implies \: \frac{2}{ \sin(a) } = 2 \csc(a)$