Question

Can someone help me with this add maths multiple choice question?

Answer 1

`x=35^@to(A)`

Explanation:

`"using the "color(blue)"cofunction identity"`

`•color(white)(x)cos(90-x)=sinx`

`cosx=cos(90-(x+20))=cos(70-x)`

`"thus "x=70-xrArr2x=70rArrx=35^@`

`"that is "sin55^@=cos35^@`

Answer 2

The answer is (a)

Explanation:

We can figure this out by first eliminating the choices that don't make sense.

(b) can't be the answer because if `x=45^@`, then `sin(x)=cos(x)` because `sin(45^@)=cos(45^@)`. Therefore, `sin(65)!=cos(45)`

(d) also cannot be the answer, because `sin(90)=1`, and `cos(70)!=1`

This leaves us with (a) and (c) for options.

If you plot `sin(x)` and `cos(x)`, you find that `sin(x)` is increasing as `xrarr90^@` and `cos(x)` is decreasing. since we know that `sin(45^@)=cos(45^@)`, It would stand to make sense that the answer should have `45^@` as a halfway mark between the evaluated answers.

graph{(y-sin((pix)/180))(y-cos((pix)/180))=0 [-90, 180, -.5, 1.5]}

Taking the average for option (a):

`(35+55)/2=90/2=45`

This looks good, lets check option (c):

`(55+75)/2=130/2=65`

This doesn't sit over 45, so our best bet is to go with option (a).