Find values for theta that make each statement true sin thet

Find values for theta that make each statement true. sin theta = cos (15) sin 55 = cos theta

Given question

sin(thete-30) = cos(theta)

Calculate the value of theta

so sin(thete-30) = cos(theta)

we know sin(a-b) = sina cosb - cosa sinb

so putting the value in the formula we get

sin thete cos30 - cos theta sin30 = cos theta

sin thete cos(sqrt3/2) - cos theta (1/2) = cos thete

putting the value of sin theta and cos theta

we get (sqrt3/2) sin theta = (1+(1/2))cos thete

there for sin theta / cos theta = 3/sqrt3 sin theta / cos theta = tan theta

tan theta = 3/sqrt3

theta = tan^-1 (3/sqrt3)

theta = 60

Answer