D.K. Ramesh Kumar and C. V. Jayanna Solutions for Chapter: Measurement of Angles and Trigonometric Functions, Exercise 1: Exercise 1

The angle of elevation of the top of a tower from the top and bottom of a building of height '$a$' are ${30}^o$ and ${45}^o$, respectively. If the tower and building stand at the same level. The height of the tower is:

$\cos 1^o+\cos 2^o+ \dots \dots \dots .+\cos {180}^o=$

If $A+B+C={180}^o$ then $\sum \tan \frac{A}{2} \tan \frac{B}{2}=$

If $\sin x+{\sin }^{2}x=1$ then ${\cos }^{12}x+3{\cos }^{10}x+3{\cos }^{8}x+{\cos }^{6}x=$

If $0\le x\le \pi$ and ${81}^{{\cos }^{2}x}+{81}^{{\sin }^{2}x}=30$ then $x=$

The value of $\cos \left({270}^o+\theta \right)\cos \left({90}^o-\theta \right)-\sin \left({270}^o-\theta \right)\cos \theta$ is:

If $12{\cot }^2\theta -31cosec\theta +32=0$ then the value of $\sin \theta$ is:

If $\left(1+\tan \theta \right)\left(1+\tan \varphi \right)=2$ then $\theta +\varphi =$