Let's solve this. We want to simplify the expression (tan x) / (cos x). Step 1: Rewrite tan x in terms of sin x and cos x. Recall that tan x = (sin x) / (cos x). So, the expression becomes: ((sin x) / (cos x)) / (cos x) Step 2: Simplify the complex fraction. Dividing by cos x is the same as multiplying by (1)/(cos x). (sin x) / (cos x) × (1) / (cos x) Step 3: Multiply the fractions. (sin x × 1) / (cos x × cos x) Step 4: Simplify the denominator. sin x / cos² x This can also be written as (sin x) × (1/cos x) × (1/cos x), which is sin x sec² x. The simplified expression for (tan x) / (cos x) is sin x / cos² x or sin x sec² x.

What of tan x /cos x

June 12, 2026Mathematics

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Let's solve this.

We want to simplify the expression (tan x) / (cos x).

Rewrite tan x in terms of sin x and cos x.
Recall that tan x = (sin x) / (cos x).
So, the expression becomes: ((sin x) / (cos x)) / (cos x)
Simplify the complex fraction.
Dividing by cos x is the same as multiplying by (1)/(cos x).
(sin x) / (cos x) × (1) / (cos x)
Multiply the fractions.
(sin x × 1) / (cos x × cos x)
Simplify the denominator.
sin x / cos² x

This can also be written as (sin x) × (1/cos x) × (1/cos x), which is sin x sec² x.

The simplified expression for (tan x) / (cos x) is sin x / cos² x or sin x sec² x.

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What of tan x /cos x

Step-by-step solution

Rewrite tan x in terms of sin x and cos x.

Simplify the complex fraction.

Multiply the fractions.

Simplify the denominator.

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