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$\theta$ = ...

If tan $\theta$ = $\frac{m^2 - n^2}{2mn}$ find sec\(\the...

If tan $\theta$ = $\frac{m^2 - n^2}{2mn}$ find sec $\theta$

A.

$\frac{m^2 + n^2}{(m^2 - n^2)}$

B.

$\frac{m^2 + n^2}{2mn}$

C.

$\frac{mn}{2(m^2 + n^2)}$

D.

$\frac{m^2n^2}{2(m^2 - n^2)}$

View answer & explanation

Correct answer is B

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

$\frac{\text{Opp}}{\text{Adj}}$ by pathagoras theorem

= Hyp² = Opp² + Adj²

Hyp² = (m² - n²) + (2mn)²

Hyp² = m⁴ - 2m²n⁴ - 4m² - n²

Hyp² = m⁴ + 2m² + n²n

Hyp² = (m² - n²)²

Hyp² = $\frac{m^2 + n^2}{2mn}$

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