Question

find the value for tan 90° , cosec 90° , sec 90° and cot 90°
reply with total explanation​

Answer 1

Step-by-step explanation:

the value of tan90 is infinity,

tan90= sin90/cos90

value of sin 90 is 1 and value of cos90 is 0 so 1/0 is infinity.

cosec90= 1/sin90=1/1=1

sec 90=1/cos90=infinity

cot90=1/tan90=0

Dear Fatima,

here you have to learn the relationship between the trignometric functions, then and then only you can solve the questions.

Answer 2

$\color{red}\huge{\underline{\underline{TO\: FIND\dag}}}$

• Tan90°
• Cosec90°
• Sec90°
• Cot90°

$\color{red}\huge{\underline{\underline{SOLUTION\dag}}}$

We know that;

$\sin(90) = 1.......(1)$

$\cos(90) = 0.......(2)$

But,we also know that;

$\tan( \theta) = \frac{ \sin( \theta) }{ \cos( \theta) }......(3)$

$\cosec ( \theta) = \frac{1}{ \sin( \theta) } ......(4)$

$\sec( \theta) = \frac{1}{ \cos( \theta) } .......(5)$

$\cot( \theta) = \frac{ \cos( \theta) }{ \sin( \theta) } .......(6)$

From (1) (2) & (3);

$\implies \tan(90) = \frac{ \sin(90) }{ \cos(90) }$

$\implies \tan(90) = \frac{1}{0}$

${ \boxed{ \color{orange} \therefore \tan(90) = \infty \: \: (or) \: \: undefined }}$

Similarly for 'cosec','sec' & 'cot';

${ \boxed{ \color{orange} \therefore \cosec(90) = 1 }}$

${ \boxed{ \color{orange} \therefore \sec(90) = \infty \: \:( or) \: \: undefined}}$

${ \boxed{ \color{orange} \therefore \cot(90) = 0}}$

HOPE THAT IS CLEAR!!

PLEASE APPRECIATE THE HARD WORK....