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Mathematics · Introduction to Trigonometry · NCERT Examples

Example 4

A complete, independently verified solution for NCERT Example 4.

Mathematics · Chapter 8 · NCERT Examples

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NCERT Example

Example 4

tan A · verification

In right triangle ABC, right-angled at B, tan A = 1. Verify that 2 sin A cos A = 1.

Isosceles right triangle ABC, right-angled at B, used to verify a trigonometric relation.
Figure 8-11 from the supplied NCERT chapter.

Solution

Board-exam working:

tan⁡A=BCAB=1⇒BC=AB\tan A=\frac{BC}{AB}=1\Rightarrow BC=AB

Let AB = BC = k.

AC=k2+k2=k2AC=\sqrt{k^2+k^2}=k\sqrt2
sin⁡A=kk2=12\sin A=\frac{k}{k\sqrt2}=\frac1{\sqrt2}
cos⁡A=kk2=12\cos A=\frac{k}{k\sqrt2}=\frac1{\sqrt2}
2sin⁡Acos⁡A=2(12)(12)=12\sin A\cos A=2\left(\frac1{\sqrt2}\right)\left(\frac1{\sqrt2}\right)=1

Final answer

Verified: 2 sin A cos A = 1.