10 points!!! Math problem (:?

Can someone please help me with this math?

Verify each trigonometric identity.

sin x + cos x = cot x +1/ csc x

and

cos x / 1+ sin x = 1- sin x/ cos x

Comments

  • 1.

    sin x + cos x multiply and divide by sinx

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

    = sin x(1 + cot x)

    Since sin x = 1/cosec x

    = (1 + cot x)/cosec x

    2. since sin^2x + cos^2x = 1

    cos^2x = 1 - sin^2x

    cos^2x = (1 + sinx)(1 - sinx)

    cosx*cosx = (1 + sinx)(1 - sinx)

    cosx/1+sinx = 1-sinx/cosx

  • 1.sinx+cosx=1/cscx+cosx then take l.c.m then 1/cscx+cosx=(1+cscx*cosx)/cscx=cotx+1/csx.

    2.cosx/1+sinx=(cosx/1+sinx)*((1-sinx)/(1-sinx)) {conjucating} this equals to (cosx*(1-sinx))/1-sinx^2 this equals to cosx(1-six) / cosx^2 this equals to i-sinx/cosx........

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