Write the trigonometric expression in terms of sine and cosine, and then simplify. tan(𝜃)sec(𝜃) − cos(𝜃)

Question

Write the trigonometric expression in terms of sine and cosine, and then simplify.

$\tan(\theta)\sec(\theta) - \cos(\theta)$

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Solution

Sure, let's break this down:

The trigonometric function tan(𝜃) can be expressed as sin(𝜃)/cos(𝜃), and sec(𝜃) is the reciprocal of cos(𝜃), which can be written as 1/cos(𝜃).

So, we can rewrite the expression tan(𝜃)sec(𝜃) − cos(𝜃) as:

(sin(𝜃)/cos(𝜃)) * (1/cos(𝜃)) - cos(𝜃)

This simplifies to:

sin(𝜃)/cos²(𝜃) - cos(𝜃)

This is the simplified form of the given trigonometric expression in terms of sine and cosine.

This problem has been solved

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