Question

The numerical value of cot 18° ( cot 72° cos square 22° +1/tan72°sec square68°) is

Answer 1

Answer:

$cot18\:(cot72\:cos^222+\frac{1}{tan72\:sec^268})=1$

Step-by-step explanation:

Formula used:

$cot\theta=\frac{1}{tan\theta}$

$sec\theta=\frac{1}{cos\theta}$

$cos\theta=sin(90-\theta)$

$cot\theta=tan(90-\theta)$

$cos^2\theta+sin^2\theta=1$

Now,

$cot18\:(cot72\:cos^222+\frac{1}{tan72\:sec^268})$

$=cot18\:(cot72\:cos^222+cot72\:cos^268)$

$=cot18\:cot72(\:cos^222+cos^268)$

$=cot18\:tan18(\:cos^222+sin^222)$ (cos68 = sin22 & cot72 = tan18 )

$=(\frac{1}{tan18})tan18(1)$

$=(1)(1)$

$=1$