Neha Tyagi and Amit Rastogi Solutions for Chapter: Introduction to Trigonometry and its Applications, Exercise 2: Exercise

If $\cos A+{\cos }^{2}A=1,$ then ${\sin }^2 A+{\sin }^4 A=1$

$\left(\tan \theta +2\right) \left(2 \tan \theta +1\right)=5 \tan \theta +{\sec }^2\theta$

If the length of the shadow of a tower is increasing, then the angle of elevation of the Sun is also increasing.

If a man standing on a platform $3 \mathrm{m}$ above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

The value of $2 \sin \theta$ can be $a+\frac{1}{a},$ where $a$ is a positive number and $a\ne 1.$

$\cos \theta =\frac{a^2+b^2}{2ab}$, where $a$ and $b$ are two distinct numbers such that $ab>0$.

The angle of elevation of the top a tower is $30°$. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled.

If the height of a tower and the distance of the point of observation from its foot, both increased by $10\%$, then the angle of elevation of its top remains unchanged.