Question

if tan theta = 1 /√3 , then evaluate

Answer 1

HELLO SWEETU !!!

tan²x + 1 = sec²x
1/3 + 1 = sec²x
sec²x = 4/3

cot²x + 1 = cosec²x
cosec²x=4


substitute in the equation above...
=[4 - 4/3]/[4 + 4/3]

= 8/3 * 3/16

=1/2


HOPE IT HELPS......

LUV U ❤❤

Answer 2

HOLA MATE !!!

HOPE THIS HELPS YOU...

To find :-
[cosec²x - sec²x] / [cosec²x + sec²x] = ?

Answer:
We know that,
=> tan²x + 1 = sec²x
then putting the values,
=> 1/3 + 1 = sec²x
=> sec²x = 4/3

and also,

=> cot²x + 1 = cosec²x
=> cosec²x=4

Step-by-step Explanation:-
Substitution and simplification in the above given equation.

=[cosec²x - sec²x] / [cosec²x + sec²x]

=[4 - 4/3]/[4 + 4/3]

= 8/3 * 3/16

=1/2

Hence,the value of above given equation is 1/2.




THANK YOU FOR THE WONDERFUL QUESTION...

#bebrainly