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

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Question

(A) Since $A$ and $B$ are complementary angles,$A + B = 90^\circ$ or $A + B = \frac{\pi}{2}$.Therefore,$\frac{A}{2} = \frac{\pi}{4} - \frac{B}{2}$.Tak

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Since $A$ and $B$ are complementary angles,$A + B = 90^\circ$ or $A + B = \frac{\pi}{2}$.Therefore,$\frac{A}{2} = \frac{\pi}{4} - \frac{B}{2}$.Taking the tangent on both sides: $	an \frac{A}{2} = 	an(\frac{\pi}{4} - \frac{B}{2})$.Using the formula $	an(x - y) = \frac{	an x - 	an y}{1 + 	an x 	an y}$,we get $	an \frac{A}{2} = \frac{1 - 	an \frac{B}{2}}{1 + 	an \frac{B}{2}}$.Now,consider the expression $(1 + 	an \frac{A}{2})(1 + 	an \frac{B}{2})$.Substituting the value of $	an \frac{A}{2}$: $(1 + \frac{1 - 	an \frac{B}{2}}{1 + 	an \frac{B}{2}})(1 + 	an \frac{B}{2})$.$= (\frac{1 + 	an \frac{B}{2} + 1 - 	an \frac{B}{2}}{1 + 	an \frac{B}{2}})(1 + 	an \frac{B}{2})$.$= (\frac{2}{1 + 	an \frac{B}{2}})(1 + 	an \frac{B}{2}) = 2$.Thus,option $A$ is correct.

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

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