prove that sec²Q +cos²Q can never be less than 2
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sec²Q + cos²Q < 2
⇒ sec²Q = 1 / cos²Q
⇒ 1 / cos²Q + cos²Q < 2
⇒ 1 + cos⁴ Q < 2 cos²Q
⇒ cos⁴Q - 2 cos²Q + 1 < 0
⇒ ( cos²Q - 1 )² < 0
✓ IMPOSSIBLE ✓
Cheers!
sec²Q + cos²Q < 2
⇒ sec²Q = 1 / cos²Q
⇒ 1 / cos²Q + cos²Q < 2
⇒ 1 + cos⁴ Q < 2 cos²Q
⇒ cos⁴Q - 2 cos²Q + 1 < 0
⇒ ( cos²Q - 1 )² < 0
✓ IMPOSSIBLE ✓
Cheers!
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