4. Here is the proof of (sin x - cos x)2 = sec2 x - tan2 x - 2sin x cos x.
What is the missing line

See Explanation Below

Step-by-step explanation:

Given

Required

Prove

To start with; we open the bracket on the left hand side

Reorder

From trigonometry;

So;

becomes

Also from trigonometry;

So,  

becomes

Proved

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.