Correct Answer - Option 4 :
\(-\dfrac{12}{25}\)
Concept:
tan x = \(\rm \frac{Perpendicular}{Base}\) = \(\rm \frac{P}{B}\)
sin x = \(\rm \frac{Perpendicular}{Hypotenuse}\) = \(\rm \frac{P}{H}\)
cos x = \(\rm \frac{Base}{Hypotenuse}\) = \(\rm \frac{B}{H}\)
By Pythagoras theorem
Hypotenuse2 = Perpendicular2 + Base2
Calculation:
Given:
\(\rm tan\:x=-\dfrac{3}{4}\)
P= 3, B = - 4
By Pythagoras theorem
H2 = P2 + B2
= 32 + (-4)2
Hypotenuse(H) = 5
sin x = \(\rm \frac{3}{5}\)
cos x = \(\rm \frac{-4}{5}\)
sin x . cos x = \(\rm \frac{3}{5} . \rm \frac{-4}{5}\) = \(\rm \frac{-12}{25}\)