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8. Introduction to Trigonometry
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निम्नलिखित को सिद्ध कीजिए :
यदि $\tan A =\frac{3}{4},$ तो $\sin A \cos A =\frac{12}{25}$ है
Option A
Option B
Option C
Option D
Solution
Given, $\quad \tan A=\frac{3}{4}=\frac{P}{B}=\frac{\text { Perpendicular }}{\text { Base }}$
Let $P=3 k$ and $B=4 k$
By Pythagoras theorem,
$H^{2}=P^{2}+B^{2}=(3 k)^{2}+(4 k)^{2}$
$=9 k^{2}+16 k^{2}=25 k^{2}$
$\Rightarrow \quad H=5 k$ [since, side cannot be negative]
$\sin A=\frac{P}{H}=\frac{3 k}{5 k}=\frac{3}{5}$ and $\cos A=\frac{B}{H}=\frac{4 k}{5 k}=\frac{4}{5}$
Now, $\sin A \cos A=\frac{3}{5} \cdot \frac{4}{5}=\frac{12}{25}$ Hence proved.
Standard 10
Mathematics
