L20 : Problems-2 - Trigonometry Functions, Mathematics, Class 11 Video Lecture

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19 now we have to prove that sine
squared 6x minus sine square for X is
good to go to sine of 2x into sine of
10x so we see here 6 plus 4 is equal to
10 and 6 minus 4 is version so we know
also know that a square minus B Square
is equal to a plus B into a minus ok
let's do this LHS is equal to sine
square 6x minus sine square for X this
we can write as sine of 6x plus is plus
sine of 4x into sine of 6x minus sine of
4x now we can use the form of sine a
plus sign we highlight here shiny plus
sign we is going to do 2 sine of a plus
B by 2 this is 6 X plus 4 X by 2 into
cos of a minus B bedroom that is 6 X
minus 4 X by 2 this thing the whole
thing into 2 sine X minus sine where the
equations coming from sine so he wants
to job with the box that is 2 of sine of
6 X minus 4 x by 2 into cos of 6 X plus
4 X by so you solve this you get 4 of
sine of 6 plus 4 by 2 10 by 2 5 X cos of
X into
sign of X and you get cos of Phi X this
is what we get
so we'll put 5x together and x2 gay them
swing it over into sine X 5 X cos of 5x
this is one term and dig to here
actually into 2 into sine X causes this
is what I have done I have taken 2 sine
5x cos 5 X + 2 sine X causes common
because I have to prove this into this
that is sine 2x into sine 10x we know
that 2 sine 5x cos 5 X is nothing but
sine of 10x that is sine of 5x plus 5 X
2 sine 5x cos x cos 5 x equal to sine of
5x + 5 X + 2 sine x cos x / 2 sine of X
plus X so this is nothing but sine of
10x into sine of 2 X and that means what
we were supposed to prove this is equal
to RHS so LHS is equal to RHS yeah prove
it what we have done the equation of
Earth in the form a square minus B
Square so we say the a square minus B
Square will be a plus B into a minus B
so we do it this in this form you use
this formula sign a plus B sine alpha
sine is cosine a plus B by 2 into cos
email u by 2 and we got the answer let's
solve for example we have to do that
cause for X 1 - 1 - 8 sine square X into
cos 1 so we can write cos of 4x again 2
cos 2 X plus X before that let me use
this formula cos of X plus y cos of X
plus 5 requests by cos boss boss want to
do things alone that this cos x cos Y
ignores the work done by Sun smile inks
tell you this formula so we can say cos
of 4x is not
but cause of 2x plus 2x and this is
nothing but cos of X to X into cos of 2
X thus here this is X this is y minus
sine of 2x into sine of Y this is
nothing but a light here is going to cos
squared 2x minus sine squared 2x now we
also know that cos square a plus sine
square a is equal to 1 so that is cos
square is equal to 1 minus sine square
and also we have rights to something in
one's 1 minus something explains we can
say this has 1 minus sine square 2x this
is cos square X cos square 2x minus sine
square X so this becomes 1 minus 2 sine
square 2x that's what we got now we know
that sine of 2x is nothing but 2 of sine
X cos x plus formula so we can say 1
minus 2 2 of sine X course X whole
square because sine squared X go to 2
sine X cos x so this becomes 1 minus 8
into sine square X and cos square X and
this is our RHS so you have tools let's
see part we have done cos 4x is good too
we have said cos 4 is equal to cos 2x
plus 2x and that is cos square 2 X minus
sine squared 2x so this becomes cos
squared 2x minus sine squared 2x + cos
squared 2x again say 1 minus sine
squared wakes and then we got 1 minus 2
sine squared X and sine 2x we can say 2
sine x cos x the whole thing is we have
to all see what is there in LHS in order
there in RHS so we have seen that inner
latches
for X or H is P of X that means we have
to break for X into X so for X p.m.
first poking into 2x plus 2x and then we
have broken 2 X into X plus X let's
solve this here we observe this this is
X 2 X 3 X that is X plus 2 X is equal to
3 X this is the option we have
so let us take 3 X common first so we
can write the same in this form court of
X caught up to X minus out of 3 X we
take common this become caught of 2x
plus our topics this we have to prove as
one this is LHS this is mh's this is
what we observe 2 X 2 1 X plus 2 is
equal to 3 X we can expand this so we
can write this in this form court of X
into cot of 2x minus court of 2x plus X
and this is nothing but court of 2x plus
cot of X so we know that cot of a plus B
this is nothing but
caught a caught B minus 1 by God a plus
cot this formula we know similarly the
same formula here so we'll just write
whatever it is here caught up eggs out
of 2x minus this we can say Cod of a
court of B so X is going to equal to 2 X
B is equal to X minus 1 by court of 2 X
plus cot of X and the whole thing is
multiplied by this one that is cut off
to X plus cos of X divide this is
canceled and you see what we get is cot
of X
this part of 2x - this is whole thing is
one
- quart of 2x quart of X plus one we see
that this - also cancer she wanting it
is 1 and this is equal to RH is how we
have saw this we have seen this express
2x equal to 3x we have observed from
this question so we have taken X common
and then he has a 3x is going to express
2x solved it not a finger cancer we got
that we have to prove that sine of n
plus 1 X into sine of M plus 2x plus cos
of n plus 1 X into cos of M goes to X is
going to cause us we can say that n plus
1 X is equal to 1 point n plus 2 X is
going to beta so this LHS we can also
say is going to sine of alpha sine of
beta plus cos order cos of theta so this
is equal to cos of a minus B we have
learned this because sine sine cos cos
sine is doing his own work cos is doing
his own work that is nothing but cos of
a minus B so here alpha is equal to n
plus 1 and Rita's get y plus 2 so
similarly we can write this as cos of n
plus 1 X minus n plus 2 X so this is
equal to cos of n plus 1 minus n minus 2
X and this will become cos of minus X
and we know cos of minus is good - cos
of X thus LHS / to Mauritius
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