If θ = m²-n²/m²+n², then what is the value of tan θ?

Correct Answer is : m2−n22mnm²-n²/2mn2mnm2−n2

Correct Answer is : m2−n22mnm²-n²/2mn2mnm2−n2

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Trigonometry Practice Test 2

Question : 2 of 22

Marks: +1, -0

\sin \theta = \frac{m^2-n^2}{m^2+n^2}

, then what is the value of tan θ?

Solution:

Concept:

Use

\sin \theta=\frac{\text{perpendicular}}{\text{hypotenuse}}

and find the base using Pythagoras theorem.

Explanation:

Given

\sin \theta=\frac{m^2-n^2}{m^2+n^2}

So, perpendicular

=m^2-n^2

and hypotenuse

=m^2+n^2

By Pythagoras theorem, base

=\sqrt{(m^2+n^2)^2-(m^2-n^2)^2}

Base

=\sqrt{4m^2n^2}=2mn

Therefore,

\tan \theta=\frac{\text{perpendicular}}{\text{base}}=\frac{m^2-n^2}{2mn}

Answer:

\tan \theta=\frac{m^2-n^2}{2mn}

, so the correct option is C.

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