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QUESTION
Q
If cos4 Θ − sin4 Θ = 2/3, then the value of 1 − 2 sin2 Θ is
If cos4 Θ − sin4 Θ = 2/3, then the value of 1 − 2 sin2 Θ is
A
1
B
04-Mar
C
01-Mar
D
02-Mar
E
01-Apr
A
1
B
04-Mar
C
01-Mar
D
02-Mar
E
01-Apr
Solution
cos4 Θ − sin4 Θ = 2/3
cos4 Θ − sin4 Θ = (cos2 Θ + sin2 Θ) (cos2 Θ − sin2...
cos4 Θ − sin4 Θ = 2/3
cos4 Θ − sin4 Θ = (cos2 Θ + sin2 Θ) (cos2 Θ − sin2 Θ)
= (1) (cos2 Θ − sin2 Θ)
= 1 − sin2 Θ − sin2 Θ
= 1 − 2 sin2 Θ
⇒ cos4 Θ − sin4 Θ = 1 − 2 sin2 Θ = 2/3
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Solution
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Keynote
cos2 Θ + sin2 Θ = 1
cos2 Θ = 1 − sin2 Θ
a2 − b2 = (a + b)(a − b)
cos2 Θ + sin2 Θ = 1
cos2 Θ = 1 − sin2 Θ
a2 − b2 = (a + b)(a − b)
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