Question

If cos theta=2x/1+x square,then tan theta

Answer 1

Answer:

1 / 2x √[ 1 + 2x - 3x^2 ]

Step-by-step explanation:

We know,

       tanθ = height / base = sinθ  / cosθ

       cosθ = base / hypotenuse

       sinθ = height / hypotenuse

       sin^2 θ + cos^2 θ = 1

       sin^2 θ = 1 - cos^2 θ

From above,

= > tanθ = sinθ / cosθ

= > cosθ = sinθ / tanθ

= > cos^2 θ = sin^2 θ / tan^2 θ     { square on both sides }

= > cos^2 θ = ( 1 - cos^2 θ ) / tan^2 θ      { from above }

= > tan^2 θ = ( 1 - cos^2 θ ) / cos^2 θ

= > tan^2 θ = [ 1 - { 2x / ( 1 + x ) }^2 ] / [ 2x / ( 1 + x ) ]^2

= > tan^2 θ = { ( 1 + x )^2 - ( 2x )^2 } / 4x^2

= > tan^2 θ = { 1 + x^2 + 2x - 4x^2 } / 4x^2

= > tanθ = 1 / 2x √[ 1 + 2x - 3x^2 ]