angle sum and difference calculator

📐 Angle Sum and Difference Calculator – Solve Trigonometric Identities with Ease

An Angle Sum and Difference Calculator helps you evaluate sine, cosine, and tangent values of compound angles using angle sum and difference identities — without manually memorizing or computing each formula.

Perfect for students, teachers, engineers, and anyone dealing with trigonometric expressions.

🧠 What Are Angle Sum and Difference Formulas?

In trigonometry, these formulas allow you to calculate trig functions of angle combinations, such as sin⁡(A+B)\sin(A + B)sin(A+B), cos⁡(A−B)\cos(A – B)cos(A−B), etc.

✅ Common Identities:

• Sine: sin⁡(A±B)=sin⁡Acos⁡B±cos⁡Asin⁡B\sin(A \pm B) = \sin A \cos B \pm \cos A \sin Bsin(A±B)=sinAcosB±cosAsinB
• Cosine: cos⁡(A±B)=cos⁡Acos⁡B∓sin⁡Asin⁡B\cos(A \pm B) = \cos A \cos B \mp \sin A \sin Bcos(A±B)=cosAcosB∓sinAsinB
• Tangent: tan⁡(A±B)=tan⁡A±tan⁡B1∓tan⁡Atan⁡B\tan(A \pm B) = \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}tan(A±B)=1∓tanAtanBtanA±tanB​

🔢 Example:

Calculate sin⁡(75∘)\sin(75^\circ)sin(75∘)

Use identity: sin⁡(75∘)=sin⁡(45∘+30∘)=sin⁡(45∘)cos⁡(30∘)+cos⁡(45∘)sin⁡(30∘)\sin(75^\circ) = \sin(45^\circ + 30^\circ) = \sin(45^\circ)\cos(30^\circ) + \cos(45^\circ)\sin(30^\circ)sin(75∘)=sin(45∘+30∘)=sin(45∘)cos(30∘)+cos(45∘)sin(30∘)

Substitute known values: =22⋅32+22⋅12=6+24= \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2} = \frac{\sqrt{6} + \sqrt{2}}{4}=22​​⋅23​​+22​​⋅21​=46​+2​​

The calculator does this instantly!

🎯 Why Use an Angle Sum & Difference Calculator?

• ✅ Saves time and reduces human error
• ✅ Supports degrees and radians
• ✅ Simplifies learning and checking homework
• ✅ Outputs exact values or decimal approximations
• ✅ Helpful in trigonometric proofs and simplification

📚 Applications

• Trigonometry & geometry classes
• Physics (wave motion, phase shifts)
• Engineering (angles in mechanics)
• Signal processing & robotics
• Advanced math competitions

❓FAQs – Angle Sum and Difference Calculator

🔹 Can I input values in radians?

✅ Yes, most calculators let you toggle between degrees and radians.

🔹 Will it show step-by-step solutions?

Many calculators do. Look for options labeled “show steps” or “detailed solution”.

🔹 What if the angle isn’t standard like 37°?

You can still input custom values — the calculator will give numerical answers using decimal approximations.

🔹 Can this be used on mobile?

Most online calculators are mobile-responsive, and some are available as apps.