sintan1sqrt3Solutionsintan1sqrt 3 Let tan1sqrt3t taking tan

sin(tan-1(-sqrt(3))

Solution

sin(tan^-1(-sqrt 3))

Let tan^-1(-sqrt3)=t

taking tan on both sides

tan(tan^-1(-sqrt 3))=tan t

-sqrt 3=tan t

tan t=- sqrt 3

tan t=-sqrt3/1

And tan theta= opposite/adjacent

Therefore opposite=-sqrt 3

And adjacent=1

Applying pythagoras theorem

opposite²+adjacent²=hypotenuse²

(-sqrt3)²+1²=hypotenuse²

3+1=hypotenuse²

Hypotenuse= sqrt 4=2

And sin theta= Opposite/ hypotenuse

Sin t= -sqrt3/2

Substituting back tan^-1(sqrt 3) for t,we get

sin(tan^-1(-sqrt 3))=-sqrt 3/2