Prove that: 70^ 20^ + cosec 20^ 70^ -2 70^ 20^ =0 - Vidyadip

Question

Prove that:
$\frac{\sin70^\circ}{\cos20^\circ}+\frac{\text{cosec 20}^\circ}{\sec70^\circ}-2\cos70^\circ\text{cosec }20^\circ=0$

✓

Answer

$\text{L.H.S}=\frac{\sin70^\circ}{\cos20^\circ}+\frac{\text{cosec 20}^\circ}{\sec70^\circ}-2\cos70^\circ\text{cosec }20^\circ$
$=\frac{\sin70^\circ}{\sin(90^\circ-20^\circ)}+\frac{\sec(90^\circ-20^\circ)}{\sec70^\circ}-2\cos70^\circ\sec70^\circ$
$=\frac{\sin70^\circ}{\sin70^\circ}+\frac{\sec70^\circ}{\sec70^\circ}-2\cos70^\circ\sec70^\circ$
$=1+1-2\times\cos70^\circ\times\frac{1}{\cos70^\circ}$
$=2-2$
$=0$
$=\text{R.H.S.}$

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