Mathematics · Introduction to Trigonometry · NCERT Examples

Example 8

A complete, independently verified solution for NCERT Example 8.

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Mathematics · Chapter 8 · NCERT Examples

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NCERT Example

Example 8

special angles · simultaneous equations

If sin(A − B) = 1/2 and cos(A + B) = 1/2, where 0° < A + B ≤ 90° and A > B, find A and B.

Special angles in A − B and A + BOne right triangle illustrates A minus B equal to 30 degrees and A plus B equal to 60 degrees. These are angle expressions, not vertex names.√312A − B = 30°A + B = 60°
Special angles in A − B and A + B — explanatory sketch (not to scale).

Solution

Board-exam working:

sin⁡(A−B)=12⇒A−B=30∘\sin(A-B)=\frac12\Rightarrow A-B=30^\circ
cos⁡(A+B)=12⇒A+B=60∘\cos(A+B)=\frac12\Rightarrow A+B=60^\circ

Adding the equations:

2A=90∘⇒A=45∘2A=90^\circ\Rightarrow A=45^\circ

Substituting in A + B = 60°:

45∘+B=60∘⇒B=15∘45^\circ+B=60^\circ\Rightarrow B=15^\circ

Final answer

A = 45° and B = 15°.

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