Worked example

Find the exact value of tan 75°

Steps

1. 75° = 45° + 30°
   Split.
2. tan(45° + 30°) = (tan 45° + tan 30°)/(1 − tan 45° tan 30°)
   Tangent of a sum. · Tangent of a sum
3. = (1 + √3/3)/(1 − √3/3)
   tan 45° = 1, tan 30° = √3/3.
4. = (3 + √3)/(3 − √3) = 2 + √3
   Multiply by the conjugate 3 + √3.

Identities used

• Tangent of a sum — When the problem is written in tangents — slopes of two lines, angles between lines, or exact values like tan 75°. Divide the sine sum by the cosine sum and this is what falls out.

Check it yourself

Open the verifier with the main identity pre-filled — substituting your own numbers into a step is the fastest way to find out which line you did not follow.

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