Laws

Question 1

cosA

Answer 1

b²+c²-a²
2bc

Question 2

cosB

Answer 2

c²+a²-b²
2ca

Question 3

cosC

Answer 3

a²+b²-c²
2ab

Question 4

a

Answer 4

bcosC + ccosB

Question 5

b

Answer 5

ccosA + acosC

Question 6

c

Answer 6

acosB + bcosA

Question 7

tan(B-C)/2

Answer 7

(b-c)/(b+c) × cot(A/2)

Question 8

tan(C-A)/2

Answer 8

(c-a)/(c+a) × cot(B/2)

Question 9

tan(A-B)/2

Answer 9

(a-b)/(a+b) × cot(C/2)

Question 10

sin(A/2)

Answer 10

√{(s-b)(s-c)/bc)}

Question 11

sin(B/2)

Answer 11

√{(s-c)(s-a)/ca}

Question 12

sin(C/2)

Answer 12

√{(s-a)(s-b)/ab}

Question 13

cos(A/2)

Answer 13

√{s(s-a)/bc}

Question 14

cos(B/2)

Answer 14

√{s(s-b)/ca}

Question 15

cos(C/2)

Answer 15

√{s(s-c)/ab}

Question 16

tan(A/2)

Answer 16

√{(s-b)(s-c)/s(s-a)}

Question 17

tan(B/2)

Answer 17

√{(s-c)(s-a)/s(s-b)}

Question 18

tan(C/2)

Answer 18

√{(s-a)(s-b)/s(s-c)}

Question 19

∆

Answer 19

1/2 × (product of any two sides) × (sine of the included angle)

e.g.

1/2 × bc sinA

Question 20

∆ in terms of sides

Answer 20

(1/4) × {2a²b² + 2b²c² + 2c²a² - a⁴ - b⁴ - c⁴} ^½

Question 21

∆ in terms of s

Answer 21

√{s(s-a)(s-b)(s-c)}