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well cos(60) and sec(30) and tan(45) can all be evaluated using the unit circle

http://buildingaunitcircle.weebly.com/uploads/6/2/2/3/622393/9409299.gif

Use the trig table........

do you need help using that chart above ?

....
I need to the values
like cos = 1/2
and all.......

cos(60)=1/2 that is correct
so squaring both sides gives
cos^2(60)=1/4

sec(30) means you need to find cos(30) and flip whatever number that is

\[5 \cos^2(60)+4\sec^2(30)-\tan^2(45) \\ 5(\frac{1}{4})+4(\frac{1}{\cos(30)})^2-1\]

so you still need to find cos(30)

4/3 = sec^2(30)

that can be simplify just be doing a few multiplications and additions(subtractions)

\[\frac{ 5 }{ 4 } +\frac{ 16 }{ 3 } - 1\]

right so far

shall I take LCM?

yes which the lcm(4,3,1)=12

67/12

looks awesome!

and totally correct :)

Thanks!
Please help me a bit more?

Sure. I can take a stab at it.

\[\frac{ cotA-1 }{ 2 -\sec^2(A) } = \frac{ \cot A }{ 1 + tanA }\]

Help me?

I'm suppose to use LHS and get RHS

ok then get rid of the compound fraction action on the the left hand side

\[\frac{ \cos(a) - \sin(a) }{ \sin(a) }\]

and for the denominator
2sin^(a)/cos^2(a)

that is I used \[\cos(2a)=\cos^2(a)-\sin^2(a) \\ \text{ and also } \cos(2a)=2\cos^2(a)-1\]

so the key in our proof was the use of double angle identity for cosine

Nice..
Thanks...
I need help in quadratic equations too...

ok let's see it

I honestly haven't given it a try

wait what does that mean
what is the angle of elevation 60 or 30?

and what is 30?

from 60 to 30 in secs
from the smae point

oh the angle of elevation changed from 60 to 30 in 10 sec
gotcha

|dw:1436680212196:dw|

|dw:1436680529581:dw|

wait my drawing is off

I will just make two separate drawings
|dw:1436680577539:dw|
|dw:1436680738212:dw|

We need to find the distance the plane has flown for both pictures

notice that is x for the first drawing and B for the second drawing

How to find the dist?

you can use a trig ratio

for example you are given the height which is 1km (the opposite side of the angle of elevation)

opp/adj is the tangent ratio

Thanks.
I will manage the rest...

oh your question says to put it an hours

lol

just let me know if you need any further help with this one

or if you want me to check your answer