Math, asked by aditya5832, 11 months ago

1 - tan²Φ/
1 + tan²Φ
=(cos²Φ-sin²Φ)​ prove that

Answers

Answered by Anonymous
60

Solution :-

Q : 1 - tan²Φ/1 + tan²Φ = (cos²Φ - sin²Φ)

L.H.S, 1 - tan²Φ/1 + tan²Φ

= [{1 - sin²Φ/cos²Φ}/{1 + sin²Φ/cos²Φ}]

= [{(cos²Φ - sin²Φ)/cos²Φ}/{(cos²Φ + sin²Φ)/cos²Φ}]

= [{(cos²Φ - sin²Φ)cos²Φ}/{(cos²Φ + sin²Φ)cos²Φ}]

= [{(cos²Φ - sin²Φ)}/{(cos²Φ + sin²Φ)}]

By using trigonometric identity,

cos²Φ + sin²Φ = 1

= (cos²Φ - sin²Φ)/1

= (cos²Φ - sin²Φ) ________R.H.S

Hence, Proved

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