Question

plzzz prove it with explanation

inverse trigonometry class 12​

Answer 1

❥︎Answer

To prove : tan-1(1/4) +tan-1(2/9)=sin-1(1/√5)Taking LHS : tan-1(1/4) +tan-1(2/9)>Using formula : tan-1(a) +tan-1(b)tan-1{(1/4+2/9) /1-(1/4)*(2/9)} =tan-1{(9+8)/(36-2)}

=tan-1{17/34}

=tan-1(1/2)

=Let tan-1(1/2)=x••••••••••••(eq1)tanx=1/2By applying pythagoras theorem

sinx=1/√5x

=sin-1(1/√5)••••••••••••(eq2)From (eq1) and (eq2),tan-1(1/2)

=sin-1(1/√5)..........which is RHS❣︎

Hence proved

Step-by-step explanation:

Hope its helpful to u ✌️