Question

-6) Prove that tan(1/2 sin^-1 3/4)=4-1773
​

Answer 1

Let tan

−1

(1)=x

⇒1=tanx

Let tan

−1

(2)=y

⇒2=tany

Let tan

−1

(3)=z

⇒3=tanz

tan(x+y+z)=

1−tanx.tany−tanx.tanz−tany.tanz

tanx+tany+tanz−tanx.tany.tanz

=

1−1×2−1×3−2×3

1+2+3−1×2×3

=0

⇒x+y+z=π

tan

−1

(1)+tan

−1

(2)+tan

−1

(3)=π

( x+y+z cannot be equal to zero, because

tan

−1

(1)+tan

−1

(2)+tan

−1

(3) will have some value greater than zero )