tan (x-(π/2)) ⋅ cos ((3 π/2)+x)- sin 3((7 π/2)-x) cos (x-(π/2)) ⋅ tan ((3 π/2)+x) when simplified reduces to:

Question

tan (x-(π/2)) ⋅ cos ((3 π/2)+x)- sin 3((7 π/2)-x) cos (x-(π/2)) ⋅ tan ((3 π/2)+x) when simplified reduces to: (A)  sin x cos x (B) - sin 2 x (C) - sin x cos x (D)  sin 2 x

Tardigrade Admin · Accepted Answer

((- cot x) sin x+ cos 3 x/ sin x(- cot x))=(- cos x/- cos x)(1- cos 2 x)= sin 2 x

Q. $tan (x - \frac{π}{2}) \cdot cos (\frac{3 π}{2} + x) - sin^{3} (\frac{7 π}{2} - x)$ $cos (x - \frac{π}{2}) \cdot tan (\frac{3 π}{2} + x)$ when simplified reduces to:

$sin x cos x$

$- sin^{2} x$

$- sin x cos x$

$sin^{2} x$

$\frac{( - c o t x ) s i n x + c o s ^{3} x}{s i n x ( - c o t x )} = \frac{- c o s x}{- c o s x} (1 - cos^{2} x) = sin^{2} x$

Q. tan(x−2π​)⋅cos(23π​+x)−sin3(27π​−x) cos(x−2π​)⋅tan(23π​+x) when simplified reduces to:

sinxcosx

−sin2x

−sinxcosx

sin2x