trigonometric formulae

Question 1

sin^2θ +cos^2θ =

Answer 1

1

Question 2

sec^2θ -tan^2θ

Answer 2

1

Question 3

cosec^2θ-cot^2θ

Answer 3

1

Question 4

sin(A+B)

Answer 4

sinAcosB+cosAsinB

Question 5

sin(A-B)

Answer 5

sinAcosB-cosAsinB

Question 6

cos(A+B)`

Answer 6

cosAcosB-sinAsinB

Question 7

cos(A-B)`

Answer 7

cosAcosB+sinAsinB

Question 8

tan⁡(A+B)=

Answer 8

(tan⁡A+tan⁡B)/(1-tan⁡Atan⁡B)

Question 9

tan⁡(A-B)=

Answer 9

(tan⁡A-tan⁡B)/(1+tan⁡Atan⁡B)

Question 10

cot⁡(A+B)=

Answer 10

(cot⁡Acot⁡B-1)/(cot⁡A+cot⁡B)

Question 11

) cot⁡(A-B)=

Answer 11

(cot⁡Acot⁡B+1)/(cot⁡B-cot⁡A)

Question 12

sin⁡2A

Answer 12

=(2tan^2⁡A)/(1+tanA)=2sin⁡Acos⁡A

Question 13

cos⁡2A

Answer 13

=cos^2⁡A-sin^2⁡A=(1-tan^2⁡A)/(1+tan^2⁡A)

=2cos^2⁡A-1=1-2sin^2⁡A

Question 14

tan⁡2A

Answer 14

=(2tan⁡A)/(1-tan^2⁡A)

Question 15

sin⁡3A=

Answer 15

3sin⁡A-4sin^3⁡A

Question 16

cos⁡3A=

Answer 16

4cos^3⁡A-3cos⁡A

Question 17

tan⁡3A=

Answer 17

(3tan⁡A-tan^3⁡A)/(1-3tan^2⁡A)

Question 18

2sin⁡Acos⁡B=

Answer 18

sin⁡(A+B)+sin⁡(A-B)

Question 19

2cos⁡Asin⁡B=

Answer 19

sin⁡(A+B)-sin⁡(A-B)

Question 20

2cos⁡Acos⁡B

Answer 20

=cos⁡(A+B)+cos⁡(A-B)

Question 21

(iv) 2sin⁡Asin⁡B

Answer 21

=cos⁡(A-B)-cos⁡(A+B)

Question 22

(v) sin⁡C+sin⁡D=

Answer 22

2sin⁡(C+D)/2 cos⁡(C-D)/2

Question 23

(vi) sin⁡C-sin⁡D

Answer 23

=2cos⁡(C+D)/2 sin⁡(C-D)/2

Question 24

cos⁡C+cos⁡D

Answer 24

=2cos⁡(C+D)/2 cos⁡(C-D)/2

Question 25

( viii )cos⁡C-cos⁡D

Answer 25

=-2sin⁡(C+D)/2 sin⁡(C-D)/2

Question 26

(ix) sin⁡(A+B)sin⁡(A-B)

Answer 26

=sin^2⁡A-sin^2⁡B

Question 27

(x) cos⁡(A+B)cos⁡(A-B)=

Answer 27

cos^2⁡A-sin^2⁡B

Question 28

(xi) cos⁡Acos⁡2Acos⁡4Acos⁡BA…cos⁡2^(n-1) A

Answer 28

=1/(2^n sin⁡A) sin⁡(2^n A)

Question 29

□( ) Maximum value of acos⁡θ±bsin⁡θ

Answer 29

=√(a^2+b^2 )

Question 30

4. Minimum value of acos⁡θ±bsin⁡θ

Answer 30

=-√(a^2+b^2 )

Question 31

Maximum value of acos⁡θ±bsin⁡θ+c

Answer 31

=c+√(σ^2+b^2 )

Question 32

minimum value of acos⁡θ±bsin⁡θ+c=

Answer 32

c-√(a^2+b^2 )