Question

if b tan 30+ bcot 30=1, then B =?​

Answer 1

Answer:

b = $\frac{\sqrt{3} }{4}$

Step-by-step explanation:

tan 30 = $\frac{1}{\sqrt{3} }$

cot 30 = $\sqrt{3}$

given : b tan 30+ b cot 30=1

∴ by substituting,

b x $\frac{1}{\sqrt{3} }$ + b x $\sqrt{3}$ = 1

$\frac{b}{\sqrt{3} }$ + b$\sqrt{3}$ = 1

finding lcm and multiplying in the numerator and denominator

lcm = $\sqrt{3}$

$\frac{b}{\sqrt{3} }$ + $\frac{b\sqrt{3} }{1}$ x $\frac{\sqrt{3} }{\sqrt{3} }$ = 1

→ $\frac{b}{\sqrt{3} }$ + $\frac{3b}{\sqrt{3} }$ = 1

$\frac{b+3b}{\sqrt{3} }$= 1

b+3b = $\sqrt{3}$

4b = $\sqrt{3}$

∴ b = $\frac{\sqrt{3} }{4}$

hope it helped! please mark as brainliest <3