Question

Need help with trig!!

Answer 1

a) sin x

b) cos² x

c) sin²x

Explanation:

Step(i):-

Given that the trigonometric equation

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

we have to use trigonometric formulas

`1-cosx = 2sin^(2) ((x)/(2) )`

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

now

`tan(x)/(2) = (sin(x)/(2) )/(cos(x)/(2) )`

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

=
`(2sin^(2) ((x)/(2) ) ))/(sinx )`

=
`(1-cosx)/(sinx)`

Step(ii):-

`tan((x)/(2) ) + cos x tan ((x)/(2) ) = (1-cosx)/(sinx) +cosx (1-cosx)/(sinx)`

=
`(1-cosx +cosx(1-cosx))/(sinx)`

=
`(1-cosx+cosx-cos^(2) x)/(sinx)`

=
`(1-cos^(2) x)/(sinx)`

=
`(sin^(2)x )/(sinx)`

= sinx