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$\theta$ = \...

If cos $\theta$ = $\frac{a}{b}$ , find 1 + tan²...

If cos $\theta$ = $\frac{a}{b}$ , find 1 + tan² $\theta$

A.

$\frac{b^2}{a^2}$

B.

$\frac{a^2}{b^2}$

C.

$\frac{a^2 + b^2}{b^2 - a^2}$

D.

$\frac{2a^2 + b^2}{a^2 + b^2}$

View answer & explanation

Correct answer is A

cos $\theta$ = $\frac{a}{b}$ , Sin $\theta$ = $\sqrt{\frac{b^2 - a^2}{a}}$

Tan $\theta$ = $\sqrt{\frac{b^2 - a^2}{a^2}}$ , Tan ² = $\sqrt{\frac{b^2 - a^2}{a^2}}$

1 + tan² $\theta$ = 1 + $\frac{b^2 - a^2}{a^2}$

= $\frac{a^2 + b^2 - a^2}{a^2}$

= $\frac{b^2}{a^2}$

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