If `A=75^0,b=45^0,` then prove that `b+csqrt(2)=2a`

Options

A. 2a
B. 2a+1
C. 3a
D. 2a-1

Answer

A

Explanation

Given, `A=75^(@)andB=45^(@)impliesC=60^(@)`
By sine rule, `(a)/(sinA)=(b)/(sinB)=(c)/(sinC)`
`implies(a)/(sin75^(@))=(b)/(sin45^(@))=(c)/(sin60^(@))`
Now, `b+csqrt(2)=(sin45^(@))/(sin75^(@))a+sqrt(2)(sin60^(@))/(sin75^(@))a`
`=((1)/(sqrt(2)))/((sqrt(3)+1)/(2sqrt(2)))a+sqrt(2)(sqrt(3)/(2))/((sqrt(3)+1)/(2sqrt(2)))a`
`=(2)/(sqrt(3)+1)a+(2sqrt3a)/(sqrt(3)+1)=2a`