Evaluate $\frac{\tan 65^{\circ}}{\cot 25^{\circ}}$
$0$
$2$
$5$
$1$
State whether the following are true or false. Justify your answer.
$(i)$ The value of tan $A$ is always less than $1 .$
$(ii)$ $\sec A=\frac{12}{5}$ for some value of angle $A$.
Evaluate the following:
$2 \tan ^{2} 45^{\circ}+\cos ^{2} 30^{\circ}-\sin ^{2} 60^{\circ}$
Given $\sec \theta=\frac{13}{12},$ calculate all other trigonometric ratios.
In $\triangle PQR ,$ right $-$ angled at $Q , PR + QR =25\, cm$ and $PQ =5\, cm .$ Determine the values of $\sin P, \cos P$ and $\tan P$.
In triangle $ABC ,$ right -angled at $B ,$ if $\tan A =\frac{1}{\sqrt{3}},$ find the value of:
$(i)$ $\sin A \cos C+\cos A \sin C$
$(ii)$ $\cos A \cos C-\sin A \sin C$