sec(theta)+csc(theta)=(sin(theta)+cos(theta))(tan(theta)+cot(theta))

I need to prove that the equation equals the other side.
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1 Answer

sec(theta)+csc(theta)=(sin(theta)+cos(theta))(tan(theta)+cot(theta))

RHS = (sin(t) + cos(t))*(tan(t) + cot(t)) = (sin(t) + cos(t))*(sin(t)/cos(t) + cos(t)/sin(t)) = (sin(t) + cos(t))*(sin^2(t) + cos^2(t)) /((sin(t).cos(t))

RHS = (sin(t) + cos(t))*(1) / ((sin(t).cos(t)) = (1/cos(t) + 1/sin(t)) = sec(t) + csc(t) = LHS

RHS = LHS

by Level 11 User (81.5k points)

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