If A=45∘, verify that:cos2A=2cos2A−1=1−2sin2A.

A=45∘ then 2A=90∘cos2A=cos90∘=02cos2A−1=2cos245∘−1=2(21)2−1=1−1=01−sin2A=1−2sin245∘=1−2×(21)2=1−1=0∴cos2A=2cos2A−1=1−2sin2A.

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If A = 45^{}, verify that: 2A = 2^{2}A - 1 = 1 - 2 ^{2}A.

Question

If $A = 4 5^{\circ}$ , verify that:
$cos 2 A = 2 cos^{2} A - 1 = 1 - 2 sin^{2} A$ .

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Emily Discussed

A = 4 5^{\circ}

, verify that:

cos 2 A = 2 cos^{2} A - 1 = 1 - 2 sin^{2} A

12 mins ago

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12 mins ago

A = 4 5^{\circ}

then

2 A = 9 0^{\circ}

cos 2 A = cos 9 0^{\circ} = 0

2 cos^{2} A - 1 = 2 cos^{2} 4 5^{\circ} - 1

= 2 (\frac{1}{2})^{2} - 1 = 1 - 1 = 0

1 - sin^{2} A = 1 - 2 sin^{2} 4 5^{\circ} = 1 - 2 \times (\frac{1}{2})^{2} = 1 - 1 = 0

∴ cos 2 A = 2 cos^{2} A - 1 = 1 - 2 sin^{2} A

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Question Text	If $A = 4 5^{\circ}$ , verify that: $cos 2 A = 2 cos^{2} A - 1 = 1 - 2 sin^{2} A$ .
Answer Type	Text solution:1
Upvotes	150