Q. 8 A4.2( 27 Votes )

In a right angle

Answer :

We have



Given that, tan A = √3/1


And tan A is given by,




perpendicular = √3x and base = x


Then, we can use Pythagoras theorem in ∆ABC,


(hypotenuse)2 = (perpendicular)2 + (base)2


(hypotenuse)2 = (√3x)2 + (x)2


(hypotenuse)2 = 3x2 + x2 = 4x2


hypotenuse = √(4x2) = 2x


We have, AB = √3x, BC = x and AC = 2x.


Using these values,





…(i)


Similarly,



…(ii)


Also,





…(iii)


Similarly,



…(iv)


We have to solve: sin A cos C + cos A sin C.


Substituting equations (i), (ii), (iii) & (iv) in above,


sin A cos C + cos A sin C =


sin A cos C + cos A sin C = 1/4 + 3/4


sin A cos C + cos A sin C = 4/4 = 1


Thus, sin A cos C + cos A sin C = 1.


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