Question

if√3sin theta+cos theta=2, theta=?​

Answer 1

Answer:

√((√3)^2 +(1)^2)(√3/2sin theta + 1/2cos theta)=2

2(√3/2 sin theta +1/2 cos theta )=2

(√3/2sin theta +1/2cos theta)=1

since;

√3/2= cos30

1/2= sin 30

therefore

(cos30 sin theta + sin30 costheta) =1

since

cosA sinB+ sinA cosB = sin(A+B)

therefore,

sin(30+ theta)= 1

since,

1 = sin90

hence

sin(30 + theta)= sin90

(theta +30)= n pie+( -1)^n(90). ( general form of writing trigonometric equations involving sin terms)

theta= npie +(-1)^n. (90) - (30)