Question

write the value of sin²+1/1+tan²

Answer 1

$\dfrac{ sin^{2}A + 1 }{ 1 + tan^{2} }\\ \\ \\\dfrac{sin^{2}A+1}{1 + \dfrac{height^{2}}{base^{2}}}\\ \\ \\\dfrac{sin^{2}A+1}{\dfrac{ base^{2}+height^{2}}{base^{2}}}$


$\dfrac{ sin^{2}A+1}{ \dfrac{hypotenuse^{2}}{base^{2}}} \\\\\\ \dfrac{ sin^{2}A+1}{sec^{2}A}$


$\dfrac{sin^{2}A}{sec^{2}A} + \dfrac{1}{sec^{2}A}\\\\\\\dfrac{ sin^{2}A}{\frac{1}{cos^{2}A}} + \dfrac{1}{sec^{2}A}$


sin²A cos²A + cos²A

cos²A( sin²A + 1 )