The value of \(\frac{3 \tan 10^{\circ}-\tan ^3 10^{\circ}}{1-3 \tan ^2 10^{\circ}}\) is _______,

(a)

\(\frac{1}{\sqrt3}\)

(b)

\(\frac{1}{2}\)

(c)

\(\frac{\sqrt3}2\)

(d)

\(\frac{1}{\sqrt2}\)

\(\sec^{-1}\frac{2}{3}+cosec^{-1}\frac{2}{3}=\) ______.

(a)

\(\frac{-\pi}{2}\)

(b)

\(\frac{\pi}{2}\)

(c)

\(\pi\)

(d)

\(-\pi\)

If \(\tan A=\frac{1}{2}\) and \(\tan B=\frac{1}{3}\) then tan(2A + B) is equal to ______.

(a)

1

(b)

2

(c)

3

(d)

4

\(\sin\left(\cos^{-1}\frac{3}{5}\right)\) is _____.

(a)

\(\frac{3}{5}\)

(b)

\(\frac{5}{3}\)

(c)

\(\frac{4}{5}\)

(d)

\(\frac{5}{4}\)

If p sec 50^o = tan 50^o then p is _______.

(a)

cos 50^o

(b)

sin 50^o

(c)

tan 50^o

(d)

sec 50^o