# if Sin=(2theta-30degrees)= Cos=(3thetas+40degrees) then what is the value of the theta

## sin(2Ø+30°) = cos(3Ø + 40°)

we know that sin x = cos (90-x)

so sin(2Ø-30) = cos(90 - 2Ø + 30)

= cos(120 - 2Ø)

then cos(120-2Ø)=cos(3Ø+40)

3Ø+40 = 120-2Ø

5Ø = 80

Ø = 16°

or

cos(3Ø + 40) = sin(90 - 3Ø-40) = sin(50-3Ø)

then 2Ø-30 = 50-3Ø

5Ø = 80

Ø = 16 , same answer