Question

Deduce the identity of :
1+tan2θ

A secθ

B sinθ

C cosθ

D sec2θ

Answer 1

Answer on Question #51812, Math, Trigonometry

Task:

Deduce the identity of :

1+tan²θ

A secθ

B sinθ

C cosθ

D sec²θ

Answer: D sec²θ

$$1 + tg^2 \theta = 1 + \frac{\sin^2 \theta}{\cos^2 \theta} = \frac{\cos^2 \theta + \sin^2 \theta}{\cos^2 \theta} = \frac{1}{\cos^2 \theta} = \sec^2 \theta$$

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