If $∆ABC$ is right-angled at C, then the value of cos (A + B) is:

                               
1. \(0\)
2. \(1\)
3. \(\frac{1}{2}\)
4. \(\frac{\sqrt{3}}{2}\)

If a vector is inclined at angles \(\alpha ,\beta ,~\text{and}~\gamma\), with \(x\), \(y\), and \(z\)-axis respectively, then the value of \(\sin^{2}\alpha+\sin^{2}\beta+ \sin^{2}\gamma\)${}^{}$
is equal to:
1. \(0\)
2. \(1\)
3. \(2\)
4. \(\dfrac{1}{2}\)

What is the maximum value of \(5\sin\theta-12\cos\theta \text{?}\)
1. \(12\)

2. \(17\)

3. \(7\)

4. \(13\)

Which of the following trigonometric values is not possible for any angle \(\theta\)?
1. \(\sin \theta=\dfrac{3}{5}\)
2. \(\sec \theta=100\)
3. \(\mathrm{cosec} ~\theta=0.14\)
4. None of the above