Question

Use the sum and difference identities to rewrite the following expression as a trigonometric function of a single number.tan(100°) – tan(10)1 + tan(100°)tan (10)

Answer 1

`\tan 90`

Explanations:

Given the trigonometric function:

`(\tan 100-\tan 10)/(1+\tan 100\tan 10)`

According to the double angle rule in trigonometry identity;

`\tan (A-B)=(\tan A-\tan B)/(1+\tan A\tan B)`

Comparing both expressions, you can see that:

A = 100⁰

B = 10⁰

This shows that the given trigonometry identity is equivalent to:

`\tan (100-10)=(\tan100-\tan10)/(1+\tan100\tan10)`

Next is to write the trigonometry function tan(100-10) as a function of single number;

Since tan(100-10) = tan 90, hence;

`\tan 90=(\tan100-\tan10)/(1+\tan100\tan10)`