Question

if sina=√3/2 then cosa=​

Answer 1

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sinA/sinB = √3/2   

=>  sinA = (√3/2)sinB   ...............(1)

cosA/cosB = √5/2   

=>  cosA = (√5/2)cosB  ...............(2)

Squaring and adding (1) and (2),

1 = (3/4)(sinB)2 +  (5/4)(cosB)2

=> 3(sinB)2 + 5(cosB)2 = 4

=>  3(sinB)2 + 3(cosB)2+ 2(cosB)2 = 4

=> 3{(sinB)2 +  (cosB)2} +  2(cosB)2 = 4

=>  (cosB)2 = 1/2   

=>  cosB = 1/√2 or -1/√2

=> sinB = 1/√2 or -1/√2

=> sinA = √3/(2√2) or -√3/(2√2)         

from (1)

=> cosA = √5/(2√2) or -√5/(2√2)         

from (2) Hence, 

tanA + tanB =  √3/√5 + 1.