If $\cot x=-\frac{5}{12}, x$ lies in second quadrant, find the values of other five trigonometric functions.
since $\cot x=-\frac{5}{12},$ we have $\tan x=-\frac{12}{5}$
Now $\sec ^{2} x=1+\tan ^{2} x=1+\frac{144}{25}=\frac{169}{25}$
Hence $\sec x=\pm \frac{13}{5}$
since $x$ lies in second quadrant, sec $x$ will be negative. Therefore
$\sec x=-\frac{13}{5}$
which also gives
$\cos x=-\frac{5}{13}$
Further, we have
$\sin x =\tan x \cos x=\left(-\frac{12}{5}\right) \times\left(-\frac{5}{13}\right)=\frac{12}{13} $
and $\cos ec\, x =\frac{1}{\sin x}=\frac{13}{12}$
If $\sin x + {\sin ^2}x = 1,$ then ${\cos ^8}x + 2{\cos ^6}x + {\cos ^4}x = $
$\frac{{1 + \sin A - \cos A}}{{1 + \sin A + \cos A}} =$
If for real values of $x,\cos \theta = x + \frac{1}{x},$ then
$\cos 15^\circ = $
Which of the following relations is possible