The value of \tan (45+\theta/2) is

Correct Answer is : tanθ+secθ

NIMCET 2020 Question Paper with solutions

Question : 42 of 120

Marks: +1, -0

The value of

\tan (45+θ/2)

Solution:

Standard formula

\tan (θ/2+45)

=\tan (π/4+θ/2)

={\tanπ/4+\tanθ/2}/{1-\tanπ/4\tanθ/2}

={1+\tanθ/2}/{1-\tanθ/2}

={\sinθ/2+\cosθ/2}/{\cosθ/2-\sinθ/2}×{(\sinθ/2+\cosθ/2)}/{(\sinθ/2+\cosθ/2)}

={1+\sin θ}/{\cos θ}

=\sec θ+\tanθ

Go to Question:

Prev Question

Next Question