Question

(sec theta -tan theta )²= 1-sin theta /1+sin theta​

Answer 1

Step-by-step explanation:

refer to the attachment

Answer 2

⭐Solution ⭐

✏prove that ,

(sec x -tan x )² = (1-sinx )/(1+ sin x)

✏Take LHS.

= (secx -tanx )2

= (sec²x + tan²x -2sec x tan x )....(1)

✏Take RHS.

= (1-sin x)/(1+ sin x)

= (1-sinx)(1-sin x)/(1-sin x)(1+sin x)

= (1+sin²x -2 sin x)/(1-sin²x)

= (1+sin²x -2sinx )/cos²x

= (1/ cos²x )+(sin²x/cos²x)-(2sin x/cos²x)

= sec²x + tan²x -2 sec x tan x....(2)

by (1) and (2)

L.H.S.= R.H.S

✔Thats proved

✏Important Formula

♣ Sec x = 1/ cos x

♣ (sin x/ cos x)= tan x

✒Hopes its help's u.