If $\tan A =\cot B ,$ prove that $A + B =90^{\circ}$
Given that,
$\tan A =\cot B$
$\tan A=\tan \left(90^{\circ}-B\right)$
$A=90^{\circ}-B$
$A+B=90^{\circ}$
Prove that $\sec A(1-\sin A)(\sec A+\tan A)=1$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\sqrt{\frac{1+\sin A }{1-\sin A }}=\sec A +\tan A$
In $\triangle$ $ABC,$ right-angled at $B$, $AB =5\, cm$ and $\angle ACB =30^{\circ}$ (see $Fig.$). Determine the lengths of the sides $BC$ and $AC .$
$\sin 2 A=2 \sin A$ is true when $A=$
$(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta)=……….$
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