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Trigonometric Ratio(sin,cos,tan)

Question 3 If...

Question

Question 3
If $t a n A = \frac{3}{4}$ , then $s i n A . c o s A = \frac{12}{25}$

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Solution

Given, $t a n A = \frac{3}{4} = \frac{P}{B} = \frac{P e r p e n d i c u l a r}{B a s e}$

Let P = 3k and B = 4k

By Pythagoras theorem,

$H^{2} = P^{2} + B^{2} = (3 k)^{2} + (4 k)^{2}$

$= 9 k^{2} + 16 k^{2} = 25 k^{2}$

$\Rightarrow$ H=5k [since, side cannot be negative]

$∴ s i n A = \frac{P}{H} = \frac{3 k}{5 k} = \frac{3}{5} a n d c o s A = \frac{B}{H} = \frac{4 k}{5 k} = \frac{4}{5}$

Now, $s i n A c o s A = \frac{3}{5} . \frac{4}{5} = \frac{12}{25}$

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Trigonometric Ratio(sin,cos,tan)

Standard X Mathematics

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