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........
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........