If Sec theta +Tan theta =4 find sin theta , cos theta question of the day

 sintheta = -1 and 15/17

costheta=costheta=0 and 8/17

let theta be A

SecA + TanA = 4

multiply the given equation by cosA

1 + sinA = 4

sin A =3  ...........ans

again, secA + tanA =4

multiply the equation by cot A

cos²A / sinA +1 = 4

cos²A / 3 = 4-1  ( sinA = 3 )

cos²A  = 3 *3

therefore , cosA =3.............ans

@mercy...u r telling

sin A =3 

 cosA =3

sub..these values in the equation SecA + TanA = 4

then ur getting

4/3 = 4

how ?

your mistake is at

multiply the given equation by cosA

then the eqn will be

1 + sinA = 4 cosA

sec x  - tan x  = 4 ------(1)

As known : sec ²x  - tan² x  = 1

Apply : a²  - b² = (a+b) (a-b)

So : (sec x + tan x ) (sec x - tan x ) = 1

(4 ) (sec x - tan x ) = 1

=> (sec x - tan x ) = 1/4 -----------(2)

Equations : 

sec x  - tan x  = 4 ------(1)

(sec x - tan x ) = 1/4 -----------(2)

APPLYING ELIMINATION METHOD : Adding (1) + (2)

2 *sec x = 4 + (1/4)

sec x =17 / 8  Substitute in (2)

=> (17/8- tan x ) = 1/4 

We get : tan x = 15 / 8

Therefore : sec x = 17 / 8  and  tan x = 15 / 8

Now to determine (cos x)

Apply : cos x = 1/ sec x  

So : cos x = 1 / (17/8)  = 8  / 17

Therefore : cos x = 8 / 17

Now to Determine ( sin x) : 

As : tan x = 15 / 8  and cos x = 8 / 17

Apply : tan x = sin x / cos x

 =>  15 / 8 = sin x  /  (8 / 17)

sin x = 15 / 17

Therefore : sin x = 15 / 17

Finally : cos x = 8 / 17 and sin x = 15 / 17

IF YOU ARE SATISFIED DO GIVE THUMBS UP .

Correction : the Equation (1) is not sec x - tanx = 4 but it should be written : sec x + tan x = 4

Typing Error ,dont worry the solution I have given is correct. but I just made a typing mistake .