Question

Sec theta + cos theta = 2 then what is the value of sin^2 theta + tan^2 theta

Answer 1

Let theta = x.

sec x+tan x = 2…………………..(1)

We know that :-

(sec x-tan x ) (sec x+tan x) = 1.

(sec x-tan x) (2) =1.

sec x-tan x = 1/2……………………..(2)

on adding and subtracting eq.(1) & (2).

2sec x= 5/2 => sec x = 5/4.

2tan x = 3/2 => tan x = 3/4.

sin x × 1/cos x = 3/4 .

sin x× sec x =3/4.

sin x × 5/4 = 3/4 .

sin x = 3/5 .Answer.