Question

Given that sin(a+b)=sinacosb+cosasinb find the value of sin75

Answer 1

Sin 75 = Sin (30 + 45)

  = Sin 30 Cos 45 + Sin 45 Cos 30

  = (1 / 2) (1 / root2) + (1 / root2) (root3 / 2)

  = (1 / 2 root2) + (root 3 / 2 root2)

  = (1 + root3) / 2 root2

On rationalising :-

(1 + root3) (2 root2) / (2 root2) (2 root2)

(2 root2 + 2 root6) / 8

2 (root2 + root6) / 8

(root2 + root6) / 4

Therefore Sin75 = (root2 + root6) / 4

Answer 2

Answer:sin 75 =√2+√6/4

Step-by-step explanation:

Sin(75)=sin(30+45)

On comparing,sin(45+30)=sin(a+b)

Putting values,

Sin(45+30)=sin45*cos30+cos45*sin30

-> 1/√2*√3/2+ 1/√2*1/2

-> √3/2√2 + 1/2√2

-> √3 +1 / 2√2

-> √3 +1/2√2 *√2/√2 (rationalising denominator)

-> √6+√2/4

Thank You