Question

Please Anyone Help me, Tomorrow i have test. Any person helping will have God's blessing.​

Answer 1

$\huge{\mathcal{\underline{\green{SOLUTION}}}}$

$\displaystyle \: \frac{ {sin}^{2}a }{1 + {cot}^{2} a} + \frac{ {tan}^{2} a}{ {(1 + {tan}^{2}a) }^{2} } + {cos}^{2} a$

$= \displaystyle \: \frac{ {sin}^{2}a }{ {cosec}^{2} a} + \frac{ {tan}^{2} a}{ {( {sec}^{2} a) }^{2} } + {cos}^{2} a$

$= \displaystyle \: \frac{ {sin}^{2}a }{ \frac{1}{ {sin}^{2}a } } + \frac{ \frac{ {sin}^{2} a}{ {cos}^{2}a } }{( { \frac{1}{ {cos}^{2}a }) }^{2} } + {cos}^{2} a$

$= {sin}^{4} a + {sin}^{2} a \: \times {cos}^{2} a \: + {cos}^{2} a$

$= {sin}^{2} a \: ( {sin}^{2} a+ {cos}^{2} a) + {cos}^{2} a$

$= {sin}^{2} a + {cos}^{2} a$

$= 1$

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