91Ó°ÊÓ

If \(\sec x=p+\frac{1}{p}\), then \(\sec x+\tan x\) is (a) \(p\) (b) \(2 p\) (c) \(\frac{1}{4 p}\) (d) \(\frac{4}{p}\).

If \(\tan \alpha=\frac{1}{\sqrt{x\left(x^{2}+x+1\right)}} \tan \beta=\frac{\sqrt{x}}{\sqrt{\left(x^{2}+x+1\right)}}\) and \(\tan \gamma=\frac{\sqrt{\left(x^{2}+x+1\right)}}{x \sqrt{x}}\) then prove that \(\alpha+\beta=\gamma\)

If \(\sec \theta+\tan \theta=1\), then one of the roots of the equation \(a(b-c) x^{2}+b(c-a) x+c(a-b)=0\) is \(\begin{array}{llll}\text { (a) } \tan \theta & \text { (b) } \sec \theta & \text { (c) } \cos \theta & \text { (d) } \sin \theta \text {. }\end{array}\)

Prove that \(\frac{\sec 8 \theta-1}{\sec 4 \theta-1}=\tan 8 \theta . \cot 2 \theta\).