Angles and Trigonometric Functions — Quiz

Question 1 • Precalculus

Which equation can be used to prove 1 plus tangent squared of x is equal to secant squared of x ?

Answer

cosine squared of x over secant squared of x plus sine squared of x over secant squared of x is equal to 1 over secant squared of x

cosine squared of x over sine squared of x plus sine squared of x over sine squared of x is equal to 1 over sine squared of x

the fraction with numerator cosine squared x and denominator tangent squared of x plus sine squared of x over tangent squared of x is equal to 1 over tangent squared of x

cosine squared of x over cosine squared of x plus the fraction with numerator mathrm sine squared x and denominator cosine squared of x is equal to 1 over cosine squared of x

Explanation

Start with the Pythagorean identity, cos² x + sin² x = 1. Divide every term by cos² x to get cos² x/cos² x + sin² x/cos² x = 1/cos² x, which is choice D. Since cos² x/cos² x = 1, sin² x/cos² x = tan² x, and 1/cos² x = sec² x, this gives 1 + tan² x = sec² x.

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