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