3 sin square theta plus 2 cos square theta minus 1/cos square theta
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Answer:
Step-by-step explanation:
3Sin²α + 2Cos²α - 1/Cos²α
= 2Sin²α + Sin²α + 2Cos²α - 1/Cos²α
= 2Sin²α + 1 - Cos²α + 2Cos²α - 1/Cos²α
= 2Sin²α + 2Cos²α - (Cos²α + 1/Cos²α) + 1
= 2 - (Cos²α + - 1/Cos²α) + 1
= 2 - ((Cosα - 1/Cosα)² + 2) + 1
= 1 - (Cosα - 1/Cosα)²
= 1 - ((Cos²α - 1)/Cosα)²
= 1 - (-Sin²α/Cosα)²
= 1 - (SinαTanα)²
= (1 + SinαTanα)(1 - SinαTanα)
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