Question

calculate (1+tanA÷1+cosA)^2​

Answer 1

Answer:

$\huge{\boxed{\boxed{\sf{ \frac{1 + \sin(a) \times \cos(a) }{2 \cos^{3} (a) - \sin ^{2} (a) \times \cos(a) } </p><p>}}}}$

Step-by-step explanation:

$\huge{\boxed{\boxed{\underline{\sf{SOLUTION-}}}}}$

$( \frac{1 + \tan(a) }{1 + \cos(a) } )^{2} \\ = ) \frac{ {1}^{2} + { \tan }^{2} a + 2 \tan(a) }{ {1}^{2} + { \cos }^{2} a + 2 \cos(a) } \\ = ) \frac{ \sec ^{2} a + 2 \tan(a) }{1 + 1 - \sin^{2} (a) + 2 \cos(a) } \\ = ) \frac{ \sec ^{2} a+ 2 \tan(a) }{2 \cos(a) - \sin ^{2} (a) } \\ = ) \frac{ \frac{1}{ \cos^{2} (a) }+ \frac{ \sin(a) }{ \cos(a) }}{2 \cos(a) - \sin ^{2} (a) } \\ = ) \frac{ \frac{1 + \sin(a) \times \cos(a) }{ \cos^{2} (a) } }{2 \cos(a) - \sin^{2} (a) } \\ = ) \frac{1 + \sin(a) \times \cos(a) }{2 \cos^{3} (a) - \sin ^{2} (a) \times \cos(a) }$

$\huge{\boxed{\boxed{\sf{ \frac{1 + \sin(a) \times \cos(a) }{2 \cos^{3} (a) - \sin ^{2} (a) \times \cos(a) } </p><p>}}}}$