Express the ratios $\cos A ,$ tan $A$ and $\sec A$ in terms of $\sin A .$
Express the ratios $\cos A ,$ tan $A$ and $\sec A$ in terms of $\sin A .$
Since,$\cos ^{2} A+\sin ^{2} A=1,$ therefore
$\cos ^{2} A =1-\sin ^{2} A , i . e ., \cos A =\pm \sqrt{1-\sin ^{2} A }$
This gives $\quad \cos A =\sqrt{1-\sin ^{2} A }$
Hence, $\quad \tan A =\frac{\sin A }{\cos A }=\frac{\sin A }{\sqrt{1-\sin ^{2} A }}$
and $\sec A =\frac{1}{\cos A }=\frac{1}{\sqrt{1-\sin ^{2} A }}$
Similar Questions
If $\tan 2 A=\cot \left(A-18^{\circ}\right),$ where $2 A$ is an acute angle, find the value of $A .$ (in $^{\circ}$)
If $\tan 2 A=\cot \left(A-18^{\circ}\right),$ where $2 A$ is an acute angle, find the value of $A .$ (in $^{\circ}$)
In $\triangle ABC ,$ right-angled at $B , AB =24 \,cm , BC =7 \,cm .$ Determine:
$(i)$ $\sin A, \cos A$
$(ii)$ $\sin C, \cos C$
In $\triangle ABC ,$ right-angled at $B , AB =24 \,cm , BC =7 \,cm .$ Determine:
$(i)$ $\sin A, \cos A$
$(ii)$ $\sin C, \cos C$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$(\operatorname{cosec} A-\sin A)(\sec A-\cos A)=\frac{1}{\tan A+\cot A}$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$(\operatorname{cosec} A-\sin A)(\sec A-\cos A)=\frac{1}{\tan A+\cot A}$
In $\triangle$ $PQR,$ right-angled at $Q$ (see $Fig.$), $PQ =3 \,cm$ and $PR =6 \,cm$. Determine $\angle QPR$ and $\angle PRQ$.
In $\triangle$ $PQR,$ right-angled at $Q$ (see $Fig.$), $PQ =3 \,cm$ and $PR =6 \,cm$. Determine $\angle QPR$ and $\angle PRQ$.
Express the trigonometric ratios $\sin A , \sec A$ and $\tan A$ in terms of $\cot A$.
Express the trigonometric ratios $\sin A , \sec A$ and $\tan A$ in terms of $\cot A$.