if 4 cos theta - 3sin theta=5 then the value of 4 cos theta+3sin theata is
Answers
4 cos theta - 3 sin theta = 5
4/5 cos theta - 3/5 sin theta = 1
[ cos 53 = 3/5 & sin 53 = 4/5 ]
sin 53 * cos theta - cos 53 * sin theta = 1
[ sin(x-y) = cosysinx + sinycosx ]
sin( 53-theta ) = 1
53-theta = sin^-1 (1)
[ sin 90°=1 ]
53 - theta = 90
theta = -37°
Thus 4 cos theta + 3 sin theta = 4*cos (-37)° + 3*sin (-37)°
[ cos(-theta)=cos theta & sin(-theta)= -sin theta ]
= 4*cos 37° - 3*sin 37°
= 4*4/5 - 3*3/5
= 7/5
4 cos theta - 3 sin theta = 5
4/5 cos theta - 3/5 sin theta = 1
[ cos 53 = 3/5 & sin 53 = 4/5 ]
sin 53 * cos theta - cos 53 * sin theta = 1
[ sin(x-y) = cosysinx + sinycosx ]
sin( 53-theta ) = 1
53-theta = sin^-1 (1)
[ sin 90°=1 ]
53 - theta = 90
theta = -37°
Thus 4 cos theta + 3 sin theta = 4*cos (-37)° + 3*sin (-37)°
[ cos(-theta)=cos theta & sin(-theta)= -sin theta ]
= 4*cos 37° - 3*sin 37°
= 4*4/5 - 3*3/5
= 7/5