Question

(Sec a)+(tan a)=2 then find the (sin a) + (cos a)

Answer 1

Hey

Hope this helps ^_^

Just ignore the cos A = 0 part or your qn will tend upto infinity and not remain to 2 .. hence, the only possible answer is ( 7 / 5 ) ✓✓

Answer 2

HELLO DEAR,


we know that;-

1+tan²a=sec²a

=> 1= sec²a - tan²a--------(1)

in Equation,

Sec a + tana = 2-----------(2)
{multiply both side by :-(seca - tana)}

we get,


(Sec a + tana ) (seca - tana)= 2(seca - tana)

=> sec²a - tan²a = 2(seca - tana)

=> 1 = 2(seca - tana)-----using (1)

=> (seca - tana) = 1/2--------(3)

from --(2) and--(3)

we get,


Sec a - tana = 1/2
Sec a + tana = 2
_______________
2seca=1/2+2

=>2seca=5/2

=>seca=5/4. put in----(2)

=> seca=1/cosa

=>cosa =1/5/4=4/5

we get,

Sec a + tana = 2


=> 5/4+ tana = 2

=> tan a=2-5/4

=> tan a= (8-5)/ 4

=> tan a= 3/4

=> tana= sina/cos a

= > sina= tana × cosa =3/4×4/5

=> sin a = 3/5


hence we get all these values

sin a = 3/5,cosa =4/5

now put this value in the Equation,


=> sin a+ cos a

=> 3/5 + 4/5

=> (3+4)/5

=> 7/5

hence,

sin a+ cos a=7/5


I HOPE ITS HELP YOU DEAR,
THANKS