1+sinx-cosx/1+sinx+cosx=cosecx-cotx can you prove LHS=RHS?

yah i can solve it

c

ur question is

1 + sinx -cosx/1 + sinx +cosx

={1 + sinx -cosx/1 + sinx +cosx} x {1 + sinx +cosx/1 + sinx +cosx}

={1 + sinx }^2-cos^2x/{1 + sinx +cosx}^2

={1+sin^2x + 2sinx -cos^2x} / {1 + sinx +cosx}^2

[1 - cos^2x = sin^2x]

={2sin^2x + 2sinx} / {1 + sinx +cosx}^2

=2 sinx {1 + sinx} /[{1 +sinx}^2 +2{1 +sinx}cosx +cos^2x]

expanding {1 +sinx}^2

=2 sinx {1 + sinx} /[1 + sin^2x +2sinx +cos^2x +2cosx{1 +sinx}]

=2 sinx {1 + sinx} /[2 +2sinx +2cosx{1 +sinx}]

=2 sinx {1 + sinx} /[2{1 +sinx} +2cosx{1 +sinx}]

=2 sinx {1 + sinx} /[2{1 +sinx}{1 +cosx}]

= sinx /{1 +cosx}

=sinx /{1 +cosx}*{1 -cosx}/{1 -cosx}

=sinx{1 -cosx}/sin^2x

={1 - cos x}/sinx

=cosecx -cotx

that gives u the answer

cos x+a million/cot=sinx+tanx you will adjust area one to equivalent area 2. First exchange the cotx into cosx/sinx: cosx+a million/ cosx/sinx= sinx + tanx Now, turn the denominator and multiply it by skill of the numberator, so which you cancel the sins interior the 1st term, and get cosx: cosx+a million/ (sinx/cosx)= sinx + tanx Now your difficulty appears like this, so all you need to do is multiply the a million by skill of sinx/cosx, that's called tanx, and as all of us know something circumstances a million is the unique term, so which you're left with tanx: sinx +a million(sinx/cosx)= sinx + tanx Now you're finished, and you have: sinx + tanx = sinx + tanx

This is no so easy but I can try

This is not correct

numerator = 1+ sin x - cos x

= sin x + 1- cos x

= sin x + 1-(2os^2 x/2-1)

= sin x + 2- 2 cos^2 x/2

= sin x + 2 sin ^2x/2

= 2 sin x/2 cos x/2 + 2 sin ^2 x/2

= 2sin x/2(cos x/2+ sin x/2)

similarly

denominator = 1+ cos x + sin x

= 2 cos^2 x/2 + 2 sin x/2 cos x/2

= 2 cos x/2(cos x/2+ sin x/2)

by dvision LHS = (sin x/2)/ (cos x/2) = tan x/2

not cosec x

You must understand the difference between an equation and an identity.

An equation has specific solutions and an identity is true for all possible values.

when x =90 degrees

LHS =2/2=1

RHS =1

But it is not so for when x=0,45...

u were not able to solve it bcoz its not true....

LHS is not equal to RHS.

eg.. put x=0,

Nr = 1+0-1=0,

therefore,LHS=0,

but cosec0 is not equal to 0...

it is very very easy