Christian P
17 April 2023 14:23
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Christian P
17 April 2023 14:23
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Gimana caranya y kk
Gimana caranya y kk
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W. Lestari
Mahasiswa/Alumni Universitas Sriwijaya
18 April 2023 00:51
<p>Jawaban : terbukti bahwa (cot πͺ . sec<sup>2</sup>πͺ)/(1 + cot<sup>2</sup>πͺ) = tan πͺ</p><p> </p><p>Ingat kembali:</p><p>cot πͺ = (cos πͺ)/(sin πͺ)</p><p>sec πͺ = 1/(cos πͺ)</p><p>tan πͺ = (sin πͺ)/(cos πͺ)</p><p>sin<sup>2</sup>πͺ + cos<sup>2</sup>πͺ = 1</p><p> </p><p>Maka:</p><p>(cot πͺ . sec<sup>2</sup>πͺ)/(1 + cot<sup>2</sup>πͺ)</p><p>= [(cos πͺ / sin πͺ) . (1/cos<sup>2</sup>πͺ)] / [1 + (cos<sup>2</sup>πͺ / sin<sup>2</sup>πͺ)]</p><p>= [1/(sin πͺ . cos πͺ)] / [(sin<sup>2</sup>πͺ + cos<sup>2</sup>πͺ)/(sin<sup>2</sup>πͺ)]</p><p>= [1/(sin πͺ . cos πͺ)] / [1/(sin<sup>2</sup>πͺ)]</p><p>= [1/(sin πͺ . cos πͺ)] . [(sin<sup>2</sup>πͺ)/1]</p><p>= (sin πͺ)/(cos πͺ)</p><p>= tan πͺ</p><p> </p><p>Jadi, terbukti bahwa (cot πͺ . sec<sup>2</sup>πͺ)/(1 + cot<sup>2</sup>πͺ) = tan πͺ.</p>
Jawaban : terbukti bahwa (cot πͺ . sec2πͺ)/(1 + cot2πͺ) = tan πͺ
Ingat kembali:
cot πͺ = (cos πͺ)/(sin πͺ)
sec πͺ = 1/(cos πͺ)
tan πͺ = (sin πͺ)/(cos πͺ)
sin2πͺ + cos2πͺ = 1
Maka:
(cot πͺ . sec2πͺ)/(1 + cot2πͺ)
= [(cos πͺ / sin πͺ) . (1/cos2πͺ)] / [1 + (cos2πͺ / sin2πͺ)]
= [1/(sin πͺ . cos πͺ)] / [(sin2πͺ + cos2πͺ)/(sin2πͺ)]
= [1/(sin πͺ . cos πͺ)] / [1/(sin2πͺ)]
= [1/(sin πͺ . cos πͺ)] . [(sin2πͺ)/1]
= (sin πͺ)/(cos πͺ)
= tan πͺ
Jadi, terbukti bahwa (cot πͺ . sec2πͺ)/(1 + cot2πͺ) = tan πͺ.
Β· 0.0 (0)
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Nailah S
22 April 2023 08:37
<p>Gunakan identitas trigonometri ini:</p><p>1. cotx = 1/tanx</p><p>2. sin^2x =1 + tan^2x</p>
Gunakan identitas trigonometri ini:
1. cotx = 1/tanx
2. sin^2x =1 + tan^2x
Β· 0.0 (0)
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