Prove the identity 1+secA/(divide)tanA+sinA=cosecA . Find all the angles for which 1+secx=2(tanx+sinx)?

Question

the angles are between 0 degrees and 360degrees.these are two separate questions.

prove the identity 1+secA/(divide)tanA+sinA=cosecA

the first question is 1+secA (divided) tanA+secA =cosecA there is some error

the first question is 1+secA (divided) tanA+secA =cosecA there is some error in typing

Answer 1

Leave spaces between symbols. Or else periods appear after 30 characters.

Try

1 + secA (divided) tan A + Sin A

instead of
1+secA/(divide)tanA+sinA


EDIT:

OK I get you.

Answer 1:
LHS (Left hand Side) =
(1 + sec A)/(tan A + sin A)

Put sec A = 1/Cos A
and Put tan A = Sin A/Cos A

You get:

[(1 + 1/Cos A)]/[(Sin A + Sin A CosA)/Cos A]
= [(Cos A + 1)/Cos A]/[Sin A (1 + Cos A)/Cos A]
= [(Cos A + 1)/Cos A] * [Cos A/(Sin A(1 + Cos A)]
= 1/Sin A
= Cosec A
Hence proved

Answer 2:
1 + sec x = 2(tan x + sin x)
1 + 1/cos x = 2[(sin x + sin x cos x)/cos x]
(cos x + 1) = 2 sin x + 2 sin x cos x (Canceling out cos x from denominator on both sides)

cos x + 1 = 2 sin x(1 + cos x)
2 sin x = 1
sin x = 1/2

x = 30 degrees

Answer 2

cos x+a million/cot=sinx+tanx you will regulate element one to equivalent element 2. First substitute the cotx into cosx/sinx: cosx+a million/ cosx/sinx= sinx + tanx Now, turn the denominator and multiply it with the aid 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 subject sounds like this, so all you will possibly desire to do is multiply the a million with the aid of sinx/cosx, it relatively is it relatively is termed tanx, and as all of us be conscious of 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 achieved, and you have: sinx + tanx = sinx + tanx