If sin A = 5/13, then cos A = √(1 - sin 2 A) = √(1 - (5/13) 2) = 12/13. ⇒ cos A = - 12/13. (Since, the function of cos is negative in second quadrant) If cos B = 5/13, then sin B = √(1 - cos 2 B) = √(1 - (5/13) 2) = 12/13. ⇒ sin B = - 12/13. (Since, the function of sin is negative in fourth quadrant) Using composite formula : cos (A

>>Class 11>>Maths>>Trigonometric Functions>>Trigonometric Functions of Sum and Difference of Two angles>>If cos A = 4/5 , cos B = 12/13 , 3pi/Open in AppUpdated on 2022-09-05SolutionVerified by TopprA and B both lie in the IV quadrant.=> are negativei iiSolve any question of Trigonometric Functions with-Was this answer helpful? 00More From ChapterLearn with Videos Practice more questions

TheLaw of Sines. The Law of Sines (or Sine Rule) is very useful for solving triangles: a sin A = b sin B = c sin C. It works for any triangle: a, b and c are sides. A, B and C are angles. (Side a faces angle A, side b faces angle B and. side c faces angle C).
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,\[\sin\left A - B \right = \sin A \cos B - \cos A \sin B \]\[ = \frac{4}{5} \times \frac{5}{13} - \frac{3}{5} \times \frac{12}{13}\]\[ = \frac{20}{65} - \frac{36}{65}\]\[ = \frac{- 16}{65}\]
Trigonometry- Sin, Cos, Tan, Cot. A circle centered at the origin of the coordinate system and with a radius of 1 is known as a unit circle . If P is a point from the circle and A is the angle between PO and x axis then: The x -coordinate of P is called the cosine of A and is denoted by cos A ; The y -coordinate of P is called the sine of A
Here, colorgreenI^st Quadrant=> 0 all+ve sina=5/13=>cosa=sqrt1-sin^2a=sqrt1-25/169=12/13 cosb=4/5=>sinb=sqrt1-cos^2b=sqrt1-16/25=3/5 colorredisina+b=sinacosb+cosasinb colorwhiteisina+b=5/13xx4/5+12/13xx3/5=20/65+36/65=56/65 colorblueiicosa-b=cosacosb+sinasinb colorwhiteiicosa-b=12/13xx4/5+5/13xx3/5=48/65+15/65=63/65 colorvioletiiicosb/2=sqrt1+cosb/2=sqrt1+4/5/2=sqrt9/10=3/sqrt10 colororangeivsin2a=2sinacosa=2xx5/13xx12/13=120/169

13 Si cos⁡θ=3/5, ¿cuál es el valor de sin⁡θ? * A) 5/3 B) 4/5 C) 5/4 D) 1 1 Ver respuesta Publicidad Publicidad medicomotorizado26 está esperando tu ayuda. Añade tu respuesta y gana puntos. cald060421mmcsnla0 cald060421mmcsnla0 Respuesta: 4/5. Explicación paso a paso: en el examen es la b :) Publicidad

given, cosA+B=4/5, thus tanA+B=3/4 from triangle 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 = 56/33.
4. 5. Use to find the exact value of sin 105°. In Exercises 6-11, verify each identity. 6. 7. 8. 1 - cos2 x 1 + sin x = sin x sec x cot x + tan x = sin x cos x csc x = cot x 105° = 135° - 30° cos correct to four decimal places. b 2 sin 2a tan1a - b2 cos1a + b2 cos b = 5 13, 0 6 b 6 p 2 sin a = 4 5, p 2 6 a 6 p 9. 10. 11.
Given as sin A = 4/5 and cos B = 5/13 As we know that cos A = √1 – sin2 A and sin B = √1 – cos2 B, where 0 < A, B < π/2 Therefore let us find the value of sin A and cos B cos A = √1 – sin2 A = √1 – 4/52 = √1 – 16/25 = √25 – 16/25 = √9/25 = 3/5 sin B = √1 – cos2 B = √1 – 5/132 = √1 – 25/169 = √169 – 25/169 = √144/169 = 12/13 i sin A + B As we know that sin A +B = sin A cos B + cos A sin B Therefore, sin A + B = sin A cos B + cos A sin B = 4/5 × 5/13 + 3/5 × 12/13 = 20/65 + 36/65 = 20 + 36/65 = 56/65 ii cos A + B As we know that cos A +B = cos A cos B – sin A sin B Therefore, cos A + B = cos A cos B – sin A sin B = 3/5 × 5/13 – 4/5 × 12/13 = 15/65 – 48/65 = -33/65 iii sin A – B As we know that sin A – B = sin A cos B – cos A sin B Therefore, sin A – B = sin A cos B – cos A sin B = 4/5 × 5/13 – 3/5 × 12/13 = 20/65 – 36/65 = -16/65 iv cos A – B As we know that cos A - B = cos A cos B + sin A sin B Therefore, cos A - B = cos A cos B + sin A sin B = 3/5 × 5/13 + 4/5 × 12/13 = 15/65 + 48/65 = 63/65
\n \n\n sin a 4 5 cos b 5 13
SOLUTION We can write, ⇒ (3 sin θ + 6 sin 2 θ + 4 cos θ + 6 cos 2 θ) = (3 sin θ + 4 cos θ) + (6 sin 2 θ + 6 cos 2 θ) As, Maximum value of (a sin θ + b cos θ) is√ (a 2 + b 2) ⇒ Maximum value of (3 sin θ + 4 cos θ) = √ (3 2 + 4 2) = √ (9 + 16) = √25 = 5. Now, ⇒ Value of (6 sin 2 θ + 6 cos 2 θ) = 6. ∴ Maximum value
We have, sinA=45 and B=513 ∴cosA=√1−sin2A and sinB=√1−cos2B ⇒cosA=√1−452 and sinB=√1−5132sinB=√1−5132 ⇒cosA=√1−1625 and sinB=√1−25169 ⇒cosA=√25−1625 and sinB=√169−25169 ⇒cosA=√925 and sinB=√144169⇒cosA=35 and sinB=1213 Now, sinA+B=sinA cosB+cosA sinB =45×513+35×1213=2065+3665=20+3665=5665 ii We have, sinA=45 and B=513 ∴cosA=√1−sin2A and sinB=√1−cos2B ⇒cosA=√1452 and sin B=√1−5132 ⇒cosA=√1−1615 sin B=√1−25169 ⇒cosA=√25−1625 and sin B=√169−25169 ⇒cosA=√925 and sin B=√144169 cosA=35 and sinB=1213 Now, cosA+B=cosA cosB−sinA sinB =35×513−45×1213 =1565−4865 =15−4865=−3365 iii We have, sinA=45 and cosB=513 ∴cosA=√1−sin2A and sinB=√1−cos2B ⇒cosA=√1−452 and sinB=√1−5132 ⇒cosA=√1−1625 and sinB=√1−25169 ⇒cosA=√25−1625 and sinB=√169−25169 ⇒cosA=√925 and sinB=√144169 ⇒cosA=35 and sinB=1213 Now, sinA−B=sinA cosB−cosA sinB =45×513−35×1213 =2065+3665=20−3665=−1665 iv We have, sinA=45 and cosB=513 ∴cosA=√1−sin2A and sinB=√1−cos2B ⇒cosA=√1−452 sinB=√1−5132 ⇒cosA=√1−1625 and sinB=√1−25169 ⇒cosA=√25−1625 and sinB=169−25169 ⇒cosA=√925 and sinB=1213 Now, cosA−B=cosA cosB+sinA sinB =35×513+45×1213 =1565+4865 =15+4865 =6365
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    • sin a 4 5 cos b 5 13