^{-1} 2+^{-1} 3= [AP EAPCET 18 May 2024 Shift 1]

Correct Answer is : 3π43π/443π

Correct Answer is : 3π43π/443π

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Inverse Trigonometric Functions

Section: Mathematics

Question : 33 of 33

Marks: +1, -0

\tan^{-1} 2+\tan^{-1} 3=

Solution:

To solve the expression

\tan^{-1} 2+\tan^{-1} 3

, we can use the formula for the sum of inverse tangents:

\tan^{-1} a+\tan^{-1} b=\tan^{-1} \left( \frac{a+b}{1-ab} \right)

Applying this formula to our problem, we have:

\tan^{-1} 2+\tan^{-1} 3=\tan^{-1} \left( \frac{2+3}{1-2 \times 3} \right)

Simplify the fraction:

=\tan^{-1} \left( \frac{5}{1-6} \right) =\tan^{-1}(-1)

We know that

\tan^{-1}(-1)=-\frac{\pi}{4}

. However, we typically express angles in the range 0 to

\pi

. Thus:

\tan^{-1} 2+\tan^{-1} 3=\frac{3\pi}{4}

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