Trigonometric EquationMedium
Question
Let two non-collinear unit vectors 
and 
form an acute angle. A point P moves so that at any time t the positionvector 
(where O is the origin) is given by cos t + sin t. When P is farthest from origin O, let M be the length of and 
be the unit vector along . Then,
and form an acute angle. A point P moves so that at any time t the positionvector (where O is the origin) is given by cos t + sin t. When P is farthest from origin O, let M be the length of and be the unit vector along . Then, Options
A.
and M = (1 + 
)1/2
and M = (1 + )1/2B.
and M = (1 + )1/2
and M = (1 + )1/2C. and M = (1 + 2)1/2
and M = (1 + 2)1/2D. and M = (1 + 2)1/2
and M = (1 + 2)1/2Solution
= |
cos t + 
sin t|= (cos2t + sin2t + 2 cos t sin t
) -1/2=(1 + 2 cos t sin t
) -1/2= (1 + sin 2t
) -1/2∴
max= (1 + ) -1/2 when, = 
⇒
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