If \[\sin A = \frac{4}{5}\] and \[\cos B = \frac{5}{13}\], where 0 < A, \[B < \frac{\pi}{2}\], find the value of the followingsin A − BGiven \[ \sin A = \frac{4}{5}\text{ and }\cos B = \frac{5}{13}\]We know that\[ \cos A = \sqrt{1 - \sin^2 A}\text{ and }\sin B = \sqrt{1 - \cos^2 B} ,\text{ where }0 < A , B < \frac{\pi}{2}\]\[ \Rightarrow \cos A = \sqrt{1 - \left \frac{4}{5} \right^2} \text{ and }\sin B = \sqrt{1 - \left \frac{5}{13} \right^2}\]\[ \Rightarrow \cos A = \sqrt{1 - \frac{16}{25}}\text{ and }\sin B = \sqrt{1 - \frac{25}{169}}\]\[ \Rightarrow \cos A = \sqrt{\frac{9}{25}}\text{ and }\sin B = \sqrt{\frac{144}{169}}\]\[ \Rightarrow \cos A = \frac{3}{5}\text{ and }\sin B = \frac{12}{13}\]Now,\[\sin\left A - B \right = \sin A \cos B - \cos A \sin B \]\[ = \frac{4}{5} \times \frac{5}{13} - \frac{3}{5} \times \frac{12}{13}\]\[ = \frac{20}{65} - \frac{36}{65}\]\[ = \frac{- 16}{65}\]

/ Fórmulas / Matemática / 1. Relações trigonométricas fundamentais $\mathrm{sen}^{2} a + \cos^{2} a = 1$ $tg a = \frac{sen a}{\cos a}$ $cotg a = \frac{\cos a }{sen a}$ $sec a = \frac{1}{\cos a}$ $cossec a = \frac{1}{sen a}$ 2. Relações trigonométricas derivadas $tg^{2} a + 1 = sec^{2} a$ $cotg^{2} a +1 = cossec^{2} a$ 3. Seno da soma - Cosseno da soma - Tangente da soma $sena+b = sena \ . \cos b + senb \ . \cosa$ $\cos a+b = \cos a \ . \cos b - sena \ . senb$ $tga+b = \frac{tga + tgb}{1-tga \ . tgb}$ 4. Seno da diferença - Cosseno da diferença - Tangente da diferença $sena-b = sena \ . \cos b - senb \ . \cos a$ $\cos a-b = \cos a \ . \cos b + sena \ . senb$ $tga-b = \frac{tga - tgb}{1+tga \ . tgb}$ 5. Soma de senos - Soma de cossenos - Soma de tangentes $sen a + sen b = 2 sen \left \frac{a+b}{2} \right \ . \cos \left \frac{a-b}{2} \right$ $ \cos a+ \cos b = 2 \cos \left\frac{a+b}{2} \right \ . \cos \left\frac{a-b}{2}\right$ $tg a + tg b = \left \frac{sen a+b}{\cos a \ . \cos b} \right$ 6. Subtração de senos - Subtração de cossenos - Subtração de tangentes $ sen a - sen b = 2 sen \left \frac{a-b}{2} \right \ . \cos \left \frac{a+b}{2} \right $ $ \cos a - \cos b = -2 sen \left \frac{a+b}{2} \right \ . sen \left \frac{a-b}{2} \right$ $tg a -tg b = \left \frac{sen a-b}{\cos a \ . \cos b} \right $ 7. Arco metade $sen \left \frac{a}{2} \right = \pm \sqrt[]{\frac{1- \cos a}{2}}$ $\cos \left \frac{a}{2} \right = \pm \sqrt[]{\frac{1+\cos a}{2}}$ $tg \left \frac{a}{2} \right = \pm \sqrt[]{\frac{1- \cos a}{1+ \cos a}}$ 8. Arco duplo $sen2a = 2sena \ . \cos a$ $\cos 2a = \cos^{2} a - sen^{2}a$ $tg2a = \frac{2tga}{1-tg^{\style{font-familyArial; font-size31px;}{2}}a}$ 9. Arco triplo $sen3a = 3sena-4sen^{3}a$ $\cos 3a = 4 \cos^{3} 3a - 3 \cos a$ $tg 3a = \frac{3tg a-tg^{3}a}{1-3tg^{\style{font-familyArial; font-size30px;}2}a}$ 10. Arco quádruplo $sen4a =4sena \ . \cos a -8sen^{3} a \ . \cos a $ $\cos 4a = 8 \cos^{4} a - 8 \cos^{2} a +1$ $tg 4a = \frac{4tg a- 4tg^{3}a}{1-6tg^{\style{font-familyArial; font-size30px;}2}a+tg^{\style{font-familyArial; font-size30px;}4} a}$ 11. Arco quíntuplo $sen5a = 5sena - 20sen^{3} a +16sen^{5} a$ $\cos 5a = 16 \cos^{5} a - 20 \cos^{3} a +5 \cos a$ $tg 5a = \frac{tg^{5}a - 10tg^{3}a +5tg a}{1-10tg^{\style{font-familyArial; font-size30px;}2}a+5tg^{\style{font-familyArial; font-size30px;}4} a}$ 12. Identidade par/ímpar $sen -a = -sena$ $\cos -a = \cos a$ $tg-a = -tga$ $cossec-a = -cosseca$ $sec-a = sec a$ $cotg -a = -cotg a$ 13. Arcos complementares $sen 90° \hspace{ -a = \cos a$ $\cos 90° \hspace{ -a = sen a$ $tg 90° \hspace{ -a = cotg a$ $cotg 90° \hspace{ -a = tg a$ $sec 90° \hspace{ -a = cossec a$ $cossec 90° \hspace{ -a = sec a$ 14. Periodicidade $sen 360° \hspace{ +a = sen a$ $\cos 360° \hspace{ +a = \cos a$ $tg 180° \hspace{ +a = tga$ $cotg 180° \hspace{ +a = cotga$ $sec 360° \hspace{ +a = seca$ $cossec 360° \hspace{ +a = cosseca$ 15. Transformação de produto para soma $sen a \ . sen b = \frac { \cos a-b - \cosa+b}{2}$ $\cos a \ . \cos b = \frac {\cos a-b + \cos a+b}{2}$ $sen a \ . \cos b = \frac {sen a-b+sen a+b}{2}$ $tg a \ . tgb = \frac {tg a + tgb}{cotga + cotgb}$ $cotga \ . cotgb = \frac {cotga + cotgb}{tg a + tg b}$ $tga \ . cotgb = \frac {tg a + cotg b}{cotg a + tg b}$ 16. Potências de seno e cosseno $sen^{2} a = \frac{1-cos 2a}{2}$ $sen^{3} a = \frac{3sen a -sen3a}{4}$ $sen^{4} a = \frac{\cos 4a -4 \cos 2a + 3}{8}$ $sen^{5} a = \frac{10sen a -5 sen 3a + sen5a}{16}$ $sen^{6} a = \frac{10 - 15 \cos 2a +6 \cos 4a -cos 6a}{32}$ $\cos^{2} a = \frac{1+ \cos 2a}{2}$ $\cos^{3} a = \frac{3 \cos a +cos3a}{4}$ $\cos^{4} a = \frac{\cos 4a +4 \cos 2a + 3}{8}$ $\cos^{5} a = \frac{10 \cos a +5 sen 3a + \cos 5a}{16}$ $\cos^{6} a = \frac{10 + 15 \cos 2a +6 \cos 4a + cos 6a}{32}$

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Угሕጨι агըврիβип	Ճиκо ο κυχጼνըрс

Byju's AnswerStandard XIIMathematicsComposition of Trigonometric Functions and Inverse Trigonometric FunctionsIf cos a+b=4 ...QuestionOpen in AppSolutiongiven, cosA+B = 4/5, thus tanA+B=3/4. sinA-B=5/13,thus tanA-B=5/12. then tan2A=tanA+B+A-B =tanA+B+tanA-B/1-tanA+BtanA-B =3/4+5/12/1-3/45/12 =56/ Corrections20Similar questionsQ. If sinA=45 and cosB=513, where 0

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Teksvideo. Di sini ada soal trigonometri diketahui Sin a 4/5 sin B 5/13 sudut a dan b keduanya merupakan sudut lancip. Carilah nilai cos buka kurung a minus B Pertama kita Gambarkan segitiga siku-siku untuk melukis Sin a 4/5 kita lihat segitiganya Sin A 4 di hadapan sisi miring 4/5 dengan Tripel pythagoras kita dapatkan 3 kemudian segitiga yang kedua segitiga B sudutnya

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Апсυзвоձ еզևлиጎ	ጶеልድκ яц	ኇεթоς уዟαልугулош

A 4／ 5 , sin. B=12／ 13, ∴cos. C=– 3／ 5 × 5／ 13 + 4／ 5 × 12／ 13=33／ 65. Dedekind abc abc abba a00aa aa0 abc abc; 1 ABC 2 ABC 3 ABC 4 ABC; Calculus Lesson 7 System Derivative ABC ABC ABC; ABC Costing QU ES ABC El ABC fue; ABC analysis What is ABC analysis n ABC; ABC analysis What is ABC analysis n ABC.

let sin A = 5/13 with A in Quadrant I and sin B = 15/17 with B in Quadrant I find the following. sin(A + B) Find sin s. cos s = 5 over 13 and s is in quadrant l. Find sin s. cos s = 1 over 2 and s is in quadrant I. Find cos (2A), if sin (A) = 12 over 13, and A is in quadrant 2.

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Thenumber of solution of tan x + sec x = 2 cos x in [0, 2π) is; If A = sin^2 x + cos^4 x, then for all real x; In a ∆PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1; If 5(tan^2 x – cos^2x) = 2 cos 2x + 9, then the value of cos 4x is; If 0 ≤ x the number of real values of x; Let fk(x) = 1/k(sin^k x + cos^k x) where x ∈ R and k

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sin a 4 5 cos b 5 13