Question

given cos theta is equals to 21 by 29 determine the value secant theta by tan theta + cot theta

Answer 1

cos theta=21/29
cos theta=adjacent/hypotenuse
adjacent=21
hypotenuse=29
opposite side=20
so,
Tan theta=opp/adj=20/21 and cot theta=adj/opp=21/20
sec theta=hypotenuse/adj=29/21
therefore,tan theta+cot theta/sec theta=

20/21+21/20/29/21

=29/20

Answer 2

$\huge \bf{ \red{hey}}$

$\huge{ \blue{ \mathfrak{here \: is \: answer}}}$

$\bf{given - }$

$\bf{cos \theta = \frac{21}{29}}$

hence

$\bf{\cos \theta \: = \frac{base}{hypotenuse}}$

hence in triangle

base= 21 units

and

hypotenuse=29 units

hence

perpendicular
$= \sqrt{hypotenuse ^{2} -base ^{2} }$

$= \sqrt{29^{2} - 21 ^{2} }$
$= \sqrt{841 - 441}$
$= \sqrt{400}$

$\bf{20 \: units}$

hence

$\bf{ \frac{sec \theta}{tan \theta + cot \theta}}$

$\bf{sec \theta = \frac{hypotenuse}{base}}$
hence

$\bf{sec \theta = \frac{29}{21}}$

$\bf{ tan \theta = \frac{prependicular}{base}}$

$\bf{tan \theta = \frac{20}{21}}$
and

$\bf{cot \theta = \frac{base}{perpendicular}}$

$\bf{cot \theta = \frac{21}{20}}$
for more calculations

$\bf{see \: in \: pic}$

$\huge \boxed{\boxed{ \red{hope \: it \: helps}}}$
$\huge{ \mathfrak{ \blue{thanks}}}$