Question

solve it pls i will mark as brainliest

Answer 1

Given tanA = xsinB/1 - xcosB and tan B = ysinA/1 - ycosA.

We know that cotA = 1/tanA.

cotA = 1/xsinB/1 - xcosB

         = 1-xcosB/xsinB

         = 1/xsinB - xcosB/xsinB

          = 1/xsinB - cotB

CotA + cotB = 1/xsinB  -------- (1)



We know that Cot B = 1/tan B

                                   = 1/ysinA/1-ycosA

                                   = 1-ycosA/ysinA

                                   = 1/ysinA - ycosA/ysinA

                                   = 1/ysinA - cotA


Cot B + Cot A = 1/ysinA   ----------- (2).


On solving (1) & (2), we get

cotA + cotB - cotA - cotB = 1/xsinB - 1/ysinA

1/xsinB = 1/ysinA

sinA/sinB = x/y.


Hope this helps!

Answer 2

HELLO DEAR,


Given tan A = x sinB / (1 - xcos B) and
tan B = ysin A / (1 - ycos A)

⇒ tan A (1 - xcos B) = xsin B

⇒ tan A  - xtan Acos B = xsin B

⇒ tan A   = xsin B + x tan A cos B

⇒ tan A   = x(sin B +  tan A cos B)

⇒sin A / cos A = x(sin B +  (sin A / cos A) cos B)

⇒sin A = x (sin B cos A+  sin A cos B) 

⇒sin A = x sin (A + B)  ----------(1)

similarly sin B = y(sin A cos B + sin B cos A) -------(2)

sin B = y sin (A + B) -------(2)

Divide (1) by (2) we get

 sin A / sin B = x / y.


I HOPE ITS HELP YOU DEAR, :-)