Question

if sec theta + tan theta =4, then find sec theta - tan theta ​

Answer 1

Answer:

secθ - tanθ = 4                   -----> (1)

Multiplying and dividing by secθ +tanθ

 = secθ - tanθ × secθ +tanθ/secθ +tanθ

= sec²θ - tan²θ/secθ + tanθ = 4

we know that -->  sec²θ - tan²θ = 1

1/secθ + tanθ = 4

therefore ,

secθ + tanθ = 1/4                  ----> (2)

Adding equations (1) and (2) :-

secθ - tanθ = 4

secθ + tanθ = 1/4   

---------------------------

2secθ =  4 + 1/4

2secθ =   17/4

secθ =   17/4*2

        = 17/8

we know that 

cosθ =   1/secθ

        = 1/(17/8)

        = 8/17

plz mark brainiest.....