[sin 4 theta - cos 4 theta + 1] = 2 sin theta
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Hi there
We have
Sin⁴∅ - cos⁴∅
To prove ⇒ 1 - 2cos²∅
Proof :-
From :- LHS
sin⁴∅ - cos⁴∅
⇒ ( sin²∅) ² - ( cos²∅ ) ²
⇒ ( sin²∅ + cos²∅ ) ( sin²∅ - cos²∅ )
[ since , ( a + b ) ( a- b ) = a² - b² ]
and [ sin²∅ + cos²∅ = 1 ]
⇒ so, ( 1 ) ( 1 - cos²∅ - cos ²∅ )
[ since 1- cos²∅ = sin²∅ ]
⇒ 1 - 2 cos²∅ [ This is what we had to proof ]
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