Fundamental Identities Set 2

Question 1

Sum and Difference Formulas: sin

Answer 1

sin (u+v) = sinu cosv + cosu sinv
sin (u-v) = sinu cosv - cosu sinv

Question 2

Sum and Difference Formulas: cos

Answer 2

cos (u+v) = cosu cosv - sinu sinv
cos (u-v) = cosu cosv + sinu sinv

Question 3

Sum and Difference Formulas:
tan

Answer 3

tan (u+v) = (tanu+tanv) / 1-tanutanv

tan (u-v) = (tanu-tanv) / 1+ tanutanv

Question 4

Double-Angle Formulas: sin

Answer 4

sin2u = 2 sinu cosu

Question 5

Double-Angle Formulas: cos

Answer 5

cos2u = cos^2u - sin^2u
= 2cos^2u -1
= 1 - 2sin^2u

Question 6

Double-Angle Formulas: tan

Answer 6

tan2u = (2tanu)/(1-tan^2u)

Question 7

Power-Reducing Formulas: sin^2

Answer 7

sin^2u = (1-cos2u)/2

Question 8

Power Reducing Formulas: cos^2

Answer 8

cos^2 = (1+cos2u)/2

Question 9

Power Reducing Formulas: tan^2

Answer 9

tan^2u = (1-cos2u)/(1+cos2u)

Question 10

Half-Angle Formulas: sin

Answer 10

sin (u/2) = plus/minus sqrt (1-cosu)/2

Question 11

Half-Angle Formulas: cos

Answer 11

cos (u/2) = plus/minus sqrt (1+cosu)/2

Question 12

Half-Angle Formulas: tan

Answer 12

tan (u/2) = (1-cosu)/sinu
= sinu/(1+cosu)