Question

value of cos⁴a+ cos²asin²a+sin²a/cos²a+cos²asin²a+sin⁴a​

Answer 1

$\frac{\cos⁴a+ \cos²a \sin²a+ \sin²a}{ \cos²a+ \cos²a \sin²a+ \sin⁴a}$

$\implies \frac{\cos²a(\cos²a+ \sin²a)+ \sin²}{ \cos²a+ (\cos²a + \sin²a)\sin²a}$

$\purple{\sf{since : }}$

$\red{ \boxed{\sin²a + \cos²a = 1}}$

$\implies \frac{\cos²a(1)+ \sin²}{ \cos²a+ (1)\sin²a}$

$\implies \frac{\cos²a+ \sin²}{ \cos²a+ \sin²a}$

$\implies \frac{1}{ 1}$

$\orange{\therefore 1}$