Question

anybody give ch 8 formulas class 10th Trigonometry​

Answer 1

Answer:

Step-by-step explanation:

1. Sin (A+B) = SinA x CosB + CosA x SinB

2. Sin (A-B) = SinA x CosB – CosA x SinB

3. Cos (A+B) = CosA x CosB – SinA x SinB

4. Cos (A-B) = CosA x CosB + SinA x SinB

5. Tan (A+B) = (TanA + TanB)/(1 – TanA x TanB)

6. Tan (A-B) = (TanA – TanB)/(1 + TanA x TanB)

7. Sin2A = 2SinACosA

                           OR

       = 2TanA/(1+Tan2A)

 

8. Cos2A = Cos2A – Sin2A  

                   OR

          = 1 – 2Sin2A

                    OR

          = 2Cos2A – 1

                   OR

   = (1-Tan2A)/(1+Tan2A)

                                   

 

9. Sin3A = 3SinA – 4Sin3A

 

10. Cos3A = 4Cos3A – 3CosA

 

11.Tan3A = (3TanA-4Tan2A)/(1+3Tan2A)

 

12. SinA x Sin2A X Sin4A = ¼ Sin3A

 

13. CosA x Cos2A x Cos4A = ¼ Cos3A

 

14. TanA x Tan2A x Tan4A = Tan3A

Answer 2

ANSWER:

1. sin A Perpendicular/Hypotenuse

2. cos A Base/Hypotenuse

3. tan A Perpendicular/Base

4. cot A Base/Perpendicular

5. cosec A Hypotenuse/Perpendicular

6. sec A Hypotenuse/Base

Trigonometric Sign Functions

sin (-θ) = − sin θ

cos (−θ) = cos θ

tan (−θ) = − tan θ

cosec (−θ) = − cosec θ

sec (−θ) = sec θ

cot (−θ) = − cot θ

Trigonometric Identities

sin2A + cos2A = 1

tan2A + 1 = sec2A

cot2A + 1 = cosec2A

Periodic Identities

sin(2nπ + θ ) = sin θ

cos(2nπ + θ ) = cos θ

tan(2nπ + θ ) = tan θ

cot(2nπ + θ ) = cot θ

sec(2nπ + θ ) = sec θ

cosec(2nπ + θ ) = cosec θ

Complementary Ratios

Quadrant I

sin(π/2−θ) = cos θ

cos(π/2−θ) = sin θ

tan(π/2−θ) = cot θ

cot(π/2−θ) = tan θ

sec(π/2−θ) = cosec θ

cosec(π/2−θ) = sec θ

Quadrant II

sin(π−θ) = sin θ

cos(π−θ) = -cos θ

tan(π−θ) = -tan θ

cot(π−θ) = – cot θ

sec(π−θ) = -sec θ

cosec(π−θ) = cosec θ

Quadrant III

sin(π+ θ) = – sin θ

cos(π+ θ) = – cos θ

tan(π+ θ) = tan θ

cot(π+ θ) = cot θ

sec(π+ θ) = -sec θ

cosec(π+ θ) = -cosec θ

Quadrant IV

sin(2π− θ) = – sin θ

cos(2π− θ) = cos θ

tan(2π− θ) = – tan θ

cot(2π− θ) = – cot θ

sec(2π− θ) = sec θ

cosec(2π− θ) = -cosec θ

Sum and Difference of Two Angles

sin (A + B) = sin A cos B + cos A sin B

sin (A − B) = sin A cos B – cos A sin B

cos (A + B) = cos A cos B – sin A sin B

cos (A – B) = cos A cos B + sin A sin B

tan(A+B) = [(tan A + tan B)/(1 – tan A tan B)]

tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)]

Double Angle Formulas

sin2A = 2sinA cosA = [2tan A + (1+tan2A)]

cos2A = cos2A–sin2A = 1–2sin2A = 2cos2A–1= [(1-tan2A)/(1+tan2A)]

tan 2A = (2 tan A)/(1-tan2A)

Thrice of Angle Formulas

sin3A = 3sinA – 4sin3A

cos3A = 4cos3A – 3cosA

tan3A = [3tanA–tan3A]/[1−3tan2A]

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