Question

cos a cos b equal to n cos a cos b equal to n sin a by sin b equal to m then m square minus n square into sin square b​

Answer 1

HELLO DEAR,

I think your question is :-

If n= cosA/cosB and m= sinA/sinBThen show that, (m² - n² ) sin²B = (1 - n²)

NOW,

{(sin²A/sin²B) - (cos²A/cos²B)}sin²B

=> {(sin²Acos²B) - (cos²Asin²B)}/(sin²Bcos²B) × sin²B

=> {(sin²Acos²B) - (cos²Asin²B)}/(cos²B)

=> {(1 - cos²A)cos²B - cos²A(1 - cos²B)}/(cos²B)

=> {cos²B - cos²Acos²B - cos²A + cos²Acos²B}/cos²B

=> (cos²B - cos²A)/cos²B

=> 1 - cos²A/cos²B

=> 1 - (cosA/cosB)²

=> 1 - n²

HENCE, L.H.S = R.H.S

I HOPE IT'S HELP YOU DEAR,

THANKS