Question

in Sin (A + B)=equal to sinAcosB +cosAsinBand Cos (A -b )is equal to Cos A x cos b + sin a x sin b find the value of sin 75hand cos 15 ​

Answer 1

Question:

Find the value of sin75 and cos15

Solution

1. sin75 = sin(45+30)

We know that,

sin(A+B)=sinAcosB + cosAsinB

Implies,

sin75=sin45cos30+cos45sin30

»sin75 = (1/√2)(√3/2)+(1/√2)(1/2)

»sin75 = (1+√3)/2√2

2. cos15 = cos(45-30)

We know that,

cos(A-B)=cosAcosB + sinAsinB

Implies,

cos15= cos45cos30 + sin45sin30

»cos15=(1/√2)(√3/2)+(1/√2)(1/2)

»cos15= (1+√3)/2√2