Question

If alpha and beta satisfy the equation a tan tetha + a sec tetha + c=0 then prove that tan (alpha+beta)= 2ac/(c^2-a^2)

Answer 1

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Answer 2

Answer:

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atanA + bsecA =c


bsecA = c-atanA

squaring both sides,


b^2sec^2A=(c-atanA)^2

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

(b^2-a^2)tan^2A+2actanA+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)

Step-by-step explanation:

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