cos⁴θ + cos²θsin²θ + sin²θ / cos²θ + cos²θ + cos²θsin²θ + sin⁴θ = _____ .
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Step-by-step explanation:
cos⁴θ + cos²θsin²θ + sin²θ / cos²θ + cos²θ + cos²θsin²θ + sin⁴θ
= cos²θ. cos²θ + cos²θsin²θ + sin²θ / cos²θ + cos²θsin²θ + sin²θ.sin²θ
= cos²θ. ( cos²θ +sin²θ) + sin²θ / cos²θ + (cos²θ + sin²θ) . sin²θ
= cos²θ . 1 + sin²θ / cos²θ + 1 . sin²θ
= cos²θ + sin²θ / cos²θ + sin²θ = 1
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