Two adjacent sides of a parallelogram PQRS are given by PQ= j+ k and PS= i- j. If the side PS is rotated about the point P by an acute angle α in the plane of the parallelogram so that it becomes perpendicular to the side PQ, then sin ²((5α)/2)- sin ²((α)/2) is equal to:

Vector Algebra: JEE Main 2026 Mathematics question

JEE Main 2026 · 2 Apr, Evening shift · Q16

JEE Main 20262 Apr, Evening shiftMathematicsMediumVector Algebra184× since 2002

Two adjacent sides of a parallelogram PQRS are given by

\vec{PQ}=\hat j+\hat k

and

\vec{PS}=\hat i-\hat j

. If the side PS is rotated about the point P by an acute angle

\alpha

in the plane of the parallelogram so that it becomes perpendicular to the side PQ, then

\sin^2\left(\frac{5\alpha}{2}\right)-\sin^2\left(\frac{\alpha}{2}\right)

is equal to :