42. \( \frac{\sin \theta \cos \theta}{1+\cos \theta}-\frac{\sin \theta}{1-\cos \theta}=-(\cot \theta \cos \theta+\csc \theta) \) L.S. \( =\frac{(\sin \theta \cos \theta) \cdot(1-\cos \theta)-\sin \theta \cdot(1+\cos \theta)}{(1+\cos \theta)(1-\cos \theta)} \)

As part of her assignment, Devi has to use her clinometer to measure the height of an office tower \( T A \). From a point \( B \), she observes that angle \( T B A=34^{\circ} \). She then walks 25 m away from the office tower to a point \( C \) and observes that angle \( T C A=26^{\circ} \). Find the height of the sfice tover.

[1] the opposite figure: I ABO is righteangled at \( \mathrm{A}, \mathrm{A}(6,3) \) , then \( \tan (2 \mathrm{AOB})=\ldots \ldots \ldots \ldots \ldots \)

Question 36, 3.4.7 Part 1 of 3 Suppose that point \( P \) is on a circle with radius \( r \), and ray \( O P \) is rotating with angular speed \( \omega \). Complete parts (a) through (c). \( \mathrm{r}=8 \mathrm{~cm}, \omega=\frac{\pi}{8} \) radian per sec, \( t=3 \mathrm{sec} \)

\( \tan \theta=-\frac{3}{4} \), given that \( \theta \) is in quadrant IV

\( 2 \cos ^ { 2 } x - 1 \geq 0 \)