State whether the following are true or false. Justify your answer.
$\cot$ $A$ is not defined for $A =0^{\circ}$
$\cot \,A$ is not defined for $A =0^{\circ}$
As $\cot A=\frac{\cos A}{\sin A}$
$\cot 0^{\circ}=\frac{\cos 0^{\circ}}{\sin 0^{\circ}}=\frac{1}{0}=$ undefined
Hence, the given statement is true.
$\frac{1+\tan ^{2} A}{1+\cot ^{2} A}=........$
Evaluate:
$\frac{\tan 26^{\circ}}{\cot 64^{\circ}}$
If $\tan ( A + B )=\sqrt{3}$ and $\tan ( A - B )=\frac{1}{\sqrt{3}} ; 0^{\circ}< A + B \leq 90^{\circ} ; A > B ,$ find $A$ and $B$
If $\sin 3 A =\cos \left( A -26^{\circ}\right),$ where $3 A$ is an acute angle, find the value of $A= . . . . ^{\circ}$.
In $\triangle$ $OPQ$, right-angled at $P$, $OP =7\, cm$ and $OQ - PQ =1\, cm$ (see $Fig.$). Determine the values of $\sin Q$ and $\cos Q$.