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If sec $^2$ $\theta$ + tan $^2$ $\theta$ = 3, the...

If sec $^2$ $\theta$ + tan $^2$ $\theta$ = 3, then the angle $\theta$ is equal to

A.

30^o

B.

45^o

C.

60^o

D.

90^o

E.

105^o

View answer & explanation

Correct answer is B

sec $^2$ $\theta$ + tan $^2$ $\theta$ = 3

Where 1 + tan $^2$ $\theta$ = sec $^2$ $\theta$

1 + tan $^2$ $\theta$ + tan $^2$ $\theta$ = 3

2 tan $^2$ $\theta$ = 2

tan $^2$ $\theta$ = 1

tan $\theta$ = √1

where √1 = 1

tan $\theta$ = 1

And tan 45° = 1

∴ $\theta$ = 45°

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