Q. 42 D

Find the value of

, if sin A = and cos B=

Answer :

Given


We know that,



Or



Let,


Side opposite to angle A = k


and Hypotenuse = k√2


where, k is any positive integer


So, by Pythagoras theorem, we can find the third side of a triangle


(P)2 + (B)2 = (H)2


(k)2 + (B)2 = (k√2)2


k2 + (B)2 = 2k2


(B)2 = 2k2 – k2


(B)2 = k2


B =k2


B =±k [taking positive square root since, side cannot be negative]


So, Base = k


Now, we have to find the value of tan A


We know that,



So,


Now, we have to find the tan B


We know that,




Let,


Side adjacent to angle B =k√3


Hypotenuse =2k


where, k is any positive integer


So, by Pythagoras theorem, we can find the third side of a triangle


(B)2 + (P)2 = (H)2


(k√3)2 + (P)2 = (2k)2


3k2 + (P)2 = 4k2


(P)2 = 4k2 –3 k2


(P)2 = k2


P =k2


P =±k [taking positive square root since, side cannot be negative]


So, Perpendicular = k


Now, we have to find the value of sin B


We know that,



So,


Now,





Now, multiply and divide by the conjugate of √3 – 1, we get



[ (a b)(a+b) = (a2 – b2)]




2+3


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