Question

please solve it and give solution by step by step​

Answer 1

$\star\:\:\:\sf\large\underline\blue{Question:-}$

• Prove the following.

$\star\:\:\:\sf\large\underline\blue{Proof:-}$

Given,

$\sf x = \cosec( \alpha ) + \cos( \alpha )$

$\sf y = \cosec( \alpha ) - \cos( \alpha )$

Now,

$\sf x + y = 2 \cosec( \alpha )$

$\sf x - y = 2 \cos( \alpha )$

So,

$\sf( \frac{2}{x + y})^{2} + { (\frac{x - y}{2} )}^{2}$

$= { (\frac{1}{ \cosec( \alpha ) } )}^{2} + {( \frac{ \cos( \alpha ) }{1}) }^{2}$

$\sf = \sin( \alpha ) ^{2} + \cos( \alpha ) ^{2}$

$\sf = 1$

Taking RHS,

=1

Therefore,

LHS=RHS

Hence Proved.

Answer 2

Answer:

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