34. If α and β are two solutions of the equation a tan x + b secxc,

1.	34. If α and β are two solutions of the equation a tan x + b secxc, then find the values ofsin (α + β) and cos (α + β).
Answer» atan+bsec=c bsec=c-atan squaring bothsides b^2sec^2=(c-atan)^2 b^2(1+tan^2)=c^2+a^2tan^2-2actan (b^2-a^2)tan^2+2actan+b^2-c^2=0 since alpha and beta are the roots of the eq so tan(alpha)+tan(beta)=-2ac/(b^2-a^2) tan(alpha).tan(beta)=(b^2-c^2)/(b^2-a^2) tan(alpha+beta)={tan(alpha)+tan(beta)}/{1-tan(alpha).tan(beta)} =[-2ac/(b^2-a^2)]/[1-(b^2-c^2)/(b^2-a^2)] =-2ac/(c^2-a^2) =2ac/(a^2-c^2) Ans.

34. If α and β are two solutions of the equation a tan x + b secxc, then find the values ofsin (α + β) and cos (α + β).

Answer»

atan+bsec=c

bsec=c-atan

squaring bothsides

b^2sec^2=(c-atan)^2

b^2(1+tan^2)=c^2+a^2tan^2-2actan

(b^2-a^2)tan^2+2actan+b^2-c^2=0

since alpha and beta are the roots of the eq so

tan(alpha)+tan(beta)=-2ac/(b^2-a^2)

tan(alpha).tan(beta)=(b^2-c^2)/(b^2-a^2)

tan(alpha+beta)={tan(alpha)+tan(beta)}/{1-tan(alpha).tan(beta)}

=[-2ac/(b^2-a^2)]/[1-(b^2-c^2)/(b^2-a^2)]

=-2ac/(c^2-a^2)

=2ac/(a^2-c^2) Ans.