Dear Friends,
Please, help solve this maths for me:


1. Show that (1 + sin x) (1 + secant x) = Tan x
( 1 + cosine x) (1 + cosecant x)

(please, note: it is numerators (1 + sin x)(1 + secant x) over denominators 1 + cosine x) (1 + cosecant x) = Tan x)

2. Express the following angles in degrees
(i) 370 (ii) -430 10' (i.e. 10' is 10 seconds)

3. Express the following angle sin radiant
(i) 21 radiant (ii) п radiant (i.e. pie over 12)
12

Please, give details so I can learn.

Many thanks.

Kindy

Hey,

Find below solution to your problems:

1.Show that (1 + sin x) (1 + secant x) = Tan x
( 1 + cosine x) (1 + cosecant x)

(please, note: it is numerators (1 + sin x)(1 + secant x) over denominators 1 + cosine x) (1 + cosecant x) = Tan x)

Remember that secant x = 1/cosine x and cosecant x=1/sine x

therefore you can rewrite the equation as:

{(1 + sin x). (1 + 1/cosine x )}/{ ( 1 + cosine x). (1 + 1/sine x)} = Tan x

you can further simplify the numerator by rewriting (1 + sin x) (1 + 1/cosine x ) as (1 + sin x). (cosine x + 1 ).1/cosine x

(i.e (1 + 1/cosine x )= (cosine x + 1)/cosine x using cosine x as the LCM)

Likewise the denominator also becomes ( 1 + cosine x). (sine x + 1).1/sine x

thus the whole equation is rewritten as

{(1 + sin x). (cosine x + 1 ).1/cosine x}/{( 1 + cosine x). (sine x + 1).1/sine x} = tan x

simplifying further equation reduces to ,

(1/cosine x)/(1/sine x) = tan x since {(1 + sin x). (cosine x + 1 )}/{( 1 + cosine x). (sine x + 1)} reduces to 1


therefore the equation becomes

sine x/cosine x = Tan x

which shows the left hand side of the equation is equal to the right hand side.



2. i 370 = 370 degrees
ii -430 10' = -430.028 degrees


3. Angles in sine radian

A very easy way is to convert from radian to degrees and then check values on the sine tabl

formula for converting to degree is degree = Radian * 180/Pie

therefore for

i) 21 radian will be 1202.72 degree which is 0.8413 on the sine table.

ii) Pie/12 radian will be 15 degrees which is 0.2589 on the sine table.


I hope this not coming late.
Good luck

Dear Victa,
Many thanks for your kind help. I really appreciate you.

How I wish I will be a guru in Maths like you.

Thanks once more.

Best Regards.

Kindy

You are welcome

U don't need to be a guru, just know the representations and substitute,but be very cautious as well, ok?

Yes ma

lol, what are u doing here?

trying to learn some maths

so where is ya lecturer? lol

where the heck have u bn?

you are the lecturer na. . .
been away looking for dear lysaa all over the universe. . .

victa,kindy. monky de work---baboon de chop.