Question

if tanx=5÷2,find secx​

Answer 1

Answer:

tanx=5/2 then by pythagoras theorem (AB)2+(BC)2=(AC)2 then 5square +2 square =root 29

Step-by-step explanation:

then secx=hyp/adjacent =root29/5

Answer 2

√29/2

Step-by-step explanation:

Given:

$\tan x = \dfrac{5}{2}$

To find:

$\sec x$

Solution:

As We know,

${ \sec x }^{2} - \tan {}^{2} x = 1 \\ \\ Or, { \sec x }^{2} = 1 + \tan {}^{2} x \\ \\ Or, { \sec x }^{2} = 1 + { (\frac{5}{2} )}^{2} \\ \\Or, { \sec x }^{2} = 1 + \frac{25}{4} \\ \\ Or, { \sec x }^{2} = \frac{29}{4} \\ \\ Or, { \sec x }^{} = \frac{ \sqrt{29} }{2}$

Hence the required answer is √29/2 .

Some important trigonometry Rules:

sinø . cosecø = 1

cosø . secø = 1

tanø . cotø = 1

sin²ø + cos²ø = 1

cosec²ø - cot² = 1

sec²ø - tan²ø = 1