Question

sin theta - tan theta cos theta + cos (pi/2 - theta)

Answer 1

Is your question, to simplify the above expression?

Answer 2

If so then you must apply the identities.

Answer 3

cot ( theta - pi / 2 )= cos ( theta - pi / 2 ) / sin ( theta - pi / 2 )

cos ( theta - pi / 2 )= cos(theta) cos (pi/2) + sin(theta) sin (pi/2)
= cos(theta) (0) + sin(theta) (1)
= sin(theta)

sin ( theta - pi / 2 )= sin(theta) cos(pi/2) - cos(theta) sin(pi/2)
= sin(theta) (0) - cos(theta) (1)
= -cos(theta)
so you get,
cot ( theta - pi / 2 )= sin(theta) / -cos(theta)
cot ( theta - pi / 2 )= -tan(theta)

Answer 4

i hope that is right :-)

Answer 5

u guys can also recheck

Answer 6

\[\sin (\frac{ \pi }{ 2 }-\theta)=\cos \theta \]
\[\cos(\frac{ \pi }{ 2 }-\theta)=\sin \theta\]
\[\tan (\frac{ \pi }{ 2 }-\theta)=\cot \theta \]etc.