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Sec square theta - tan square theta equal to 1 |
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Answer» Answer: TO PROVE: 1 + Tan²θ = Sec²θ Tan θ = (Sin θ) / (COS θ) ∴ Tan²θ = (Sin θ / Cos θ)² ..... (1) L.H.S = 1 + Tan²θ (substituting from equation 1 we GET) L.H.S. = 1 + (sin θ/cos θ)² ∴ L.H.S = 1 + (Sin²θ / Cos²θ) ∴ L.H.S. = (Cos²θ + Sin²θ) / Cos²θ But, we KNOW that - Cos²θ + Sin²θ = 1 ∴ L.H.S. = 1 / Cos²θ ∵ 1 / Cosθ = Secθ ∴ L.H.S. = Sec²θ = R.H.S. as LHS = RHS... hence prooved 1 + Tan²θ = Sec²θ Step-by-step explanation: Hope this helps you pls MARK me the brainliest |
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