If A and B are complementary angles,then: | vedclass

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(A) Given that $A$ and $B$ are complementary angles,$A + B = 90^{\circ}$ or $A + B = \frac{\pi}{2}$.Thus,$\frac{A}{2} + \frac{B}{2} = \frac{\pi}{4}$.T

Vedclass · Accepted Answer

$(1 + 	an \frac{A}{2})(1 + 	an \frac{B}{2}) = 2$

Vedclass · Answer

(A) Given that $A$ and $B$ are complementary angles,$A + B = 90^{\circ}$ or $A + B = \frac{\pi}{2}$.Thus,$\frac{A}{2} + \frac{B}{2} = \frac{\pi}{4}$.Taking tangent on both sides: $	an(\frac{A}{2} + \frac{B}{2}) = 	an(\frac{\pi}{4}) = 1$.Using the formula $	an(x+y) = \frac{	an x + 	an y}{1 - 	an x 	an y}$,we get:$\frac{	an(A/2) + 	an(B/2)}{1 - 	an(A/2)	an(B/2)} = 1$.$	an(A/2) + 	an(B/2) = 1 - 	an(A/2)	an(B/2)$.Rearranging terms: $1 + 	an(A/2) + 	an(B/2) + 	an(A/2)	an(B/2) = 2$.Factoring the expression: $(1 + 	an(A/2))(1 + 	an(B/2)) = 2$.Therefore,option $A$ is correct.

If $A$ and $B$ are complementary angles,then:

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