If cos thetha = - 0.96 and (sec thetha) (sin thetha) >0 find the value of tan thetha

Cos (theta) = - 0.96 <0

=>

theta is either in the 2nd or third quadrant.

cos (theta) = - 0.96

=>

sec (theta) = 1/cos (theta) = - 1/0.96 <0

Given sec (theta) (sin (theta) >0

=> cos (theta) sin (theta) >0

=> cos (theta) and sin (theta) have the same sign,

=> sin (theta) <0

=>

theta is in the third quadrant. = > tan (theta) >0

Given cos (theta) = - 0.96

=>

|sin (theta) |=sqrt (1 - (-0.96) ^2) = sqrt (0.0784) = 0.28

=> sin (theta) = - 0.28

Finally,

tan (theta) = sin (theta) / cos (theta) = - 0.28/-0.96

=7/24

=0.29167 (to the fifth decimal place)