Question

if cos² -sin² =tan². Prove that cos =

1

√2 cos​

Answer 1

Step-by-step explanation:

cos²-sin² = tan²

cos ²-(1-cos²) = sin²/cos²

2cos²-1 = 1-cos²/cos²

(cos²)(2cos²-1) = 1-cos²

2cos⁴-cos²+cos² = 1

cos⁴ = 1/2

(cos²)² = 1/2

cos² = 1/√2

cos×cos = 1/√2

cos = 1/√2cos

HENCE PROVED

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