Ratio Complementary Angle Video Lecture - Class 10

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to trigonometry part 10 is brought you
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before watching this video please make
sure that you have watched part 1 to
part 9 I'm sorry Sigma by D ratio
complementary angle so when you see a
sine 90 degree minus a you get caution
when you say cos 91 sa you get signing
when you say 10 90 when I say you get
caught it then you say court 90 minus a
you get tan 8 you get sick 91 is saying
it cause I can say Kasich 90 minus in
here
that means if you have sign a you
can find sine 90 minus and there is
nothing but cos it may be very tip sine
becomes cos if you see sine becomes cos
cos becomes I can become got caught
become that this is if you see sine
become cos cos becomes sine tan become
caught card become then this is one pair
this is one pair similarly SEC become
Kasich and Kasich becomes this is one
pair sine theta you say sine 90 minus
theta they become cos theta you have cos
theta is she cause my name is secure
becomes sine theta this is one pair if
you have tan theta is a 10 90 minus
theta that becomes cot theta
you got theta x ik or 90 minus theta
that becomes tan theta
similarly for SEC and now let's go to
the proof we have to prove that sine 90
minus is heard or seen
cos 90 minus a is going to sign in and
then 90 minus is pretty common to prove
this let's take the same triangle ABC so
here if you see when I take when I say
sine 90 minus a this is nothing but
science you because let's say this is my
G this is hoping but 90 means
correct so what I have the blue sign C
is equal to costly that's what I have to
do so that define the value of cos gave
us or let me find all the values of
course a sign a court a in this triangle
I mean let me review this first so if
you were to prove this this is nothing
but cos of C is equal to sine a and this
is nothing but tan of season be 1/4 so
let me do one thing let me first find
the value of cos a sign and God so if
I'm assuming this as my reference angle
hypotenuse will be easy correct base
will be this one maybe and perpendicular
will be this one when I talk about sine
C sorry cause it cause in bhagavad on a
angle now formula is funding whether I
push on array I think one sign cause and
Han shortcut formula we got cos is going
to V by H V by H here B is nothing but V
that is a V and H is nothing but easy
let me write is rather than cut them
similarly sine a sine a is nothing but e
by h e by H and that comes out to be BC
by easy
we seem always so we'll record a nothing
but B by P because tan never the panel
Scott V by T we have is nothing here but
a B by V see if you buy this all and now
let me take C other
if I take C as the reference angle H is
same just become perpendicular
perpendicular C and this becomes B C
becomes base for C and even become
perpendicular part see why a be the
opposite of C and this VC is part of
legacy so now let's find sine C because
this thing were to prove Sciences comes
out to be nothing but P by H image here
piece PC is what a B a B my case it
similarly cos C cos these nothing but
causes V by H V by it correct base in
this case for C is VC which empties
already see favorite tanzy can nothing
but P by V cut what is the value of P P
of C is a V and V of C is busy you see
this this value are equal this values
are equal and this very cool correct so
I can say that cos C is equal to sine C
this is proof correct cos C is equal to
sign a this is food and tan C is going
to cut very simple all these three
things up she more drew steped caught
ninety minus a is good tanning shake 90
minus cos aka Kasich 90 minus is equal
to C same thing here I do this is a so C
will become 90 molestation so what we
have to prove court might even see is
nothing but a autopsy is equal to tan a
beer too cool Cigna T is nothing but say
cup C is equal to cos a K you have to
put and caustic 90 minus a is nothing
but cos x C and that has to be equal to
sick of me so we can improve all the
thing my follow me so let's take the
anger
first England leave articles if I take a
as a base angle hypotenuse if this this
becomes V is correct but hey please
become perpendicular Polly why because
this side AV is with adjacent to angle a
and side B C's opens you're finally I
have to mind tanning and a is equal to
fill you the formula here again unless
by the refresh our array if and I both
sine cos and Kasich say so tan a is
nothing but P bugging something but P by
V so here P is what BC BC PI B is
nothing but P correct
Tana is done cause a clearly-defined cos
e is nothing but H by P sine is P by H
cos a cos H by B H by P H is AC constant
for us and B here will be easy correct
similarly this is done SEC a say
everything but H by B H by B you see
here say K H by B H is constant easy and
B here is stable so I have all this done
now let me take angle B sorry angle see
why because we have three more on the
left hand side which are part and your C
chord C sexy and Kasich C let me find
God see God see here is B by B she
caught as V by V V by but for angle C
think for Jana if I take C as the frame
of reference this will become beans so
this will become base for angle C and
this will become perpendicular for and
but they can see as the favor of friends
AV becomes perpendicular and Basilica
phase so b is what base base foresees
and scan sir islam base for she is VC
and perpendicular is a correct next is
sexy sexy for sexy if you see will be H
by B H by me H is AC constant B for C is
nothing but we see this already the next
is cos x cos x cos I guess this one will
be H by P H by P it shall be easy and
help P will be P of C Z so you observe
here also this is equal this is equal
and this is also equal so what you can
say that tan a is equal to cot see this
is boom Kasich is equal to sexy sexy is
equal to boss again - and Kozik C is
equal to SEC a that is also so hence
everything is good like there is you
possess a beauty just keep in mind that
when you take angle a VC is the
perpendicular and if e is the base we
need a kegger see at the pin reference a
B is a perpendicular silver thank you
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