" 14.(i) If "tan(x)/(2)=(m)/(n)," prove than "m sin x+n cos x=n

(i) If "tan""(x)/(2)=(m)/(n) ,prove that m sin x+n cos x=n. (ii) If "tan" theta=(a)/(b) , prove that a sin 2theta+b cos 2theta=b .

If tan frac (x)(2)= m/n , prove than m sin x+n cos x=n .

If (tan x)/(2)=(m)/(n), then writhe the value fm sin x+n cos x

If tan theta=(m)/(n) , show that (m sin theta-n cos theta)/(m sin theta+n cos theta)=(m^(2)-n^(2))/(m^(2)+n^(2))

If int(dx)/(sqrt(x)(1+x))=m tan^(-1)(x^(n)), prove that m*n=1

If tan theta=(m)/(n) then (m sin theta+n cos theta)/(m sin theta-n cos theta) =

If (sin A)/(sin B)=m , and (cosA)/(cosB)=n , prove that tan A= +- m/n sqrt ((1-n^2)/(m^2-1)) .

3. Ifm tan= n tan prove that 3. If m tan (0 - 3) = n tan (0+ 27). prove that cos 20 = mtmm m +n cos 20 = 2 (m - n)

sin^(m)x.cos^(n)x