Question

In triangle ABC right angled at C if tan A =1/root 3
Then find the vaule of
$sin \: a \times cos \: b + \: cos \: a \: \times sin \: b$
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Answer 1

Step-by-step explanation:

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Answer 2

Answer:

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Ans - 1

Explanation

$tan \: a = \frac{1}{ \sqrt{3} }$

Perpendicular = 1

And adjacent = root 3

Therefore by using Pythagoras theorem

${ab}^{2} = {ac}^{2} + {bc}^{2}$

${ab}^{2} = {1}^{2} + {( \sqrt{3)} }^{2}$

${ab}^{2} = 4$

Ab = 2

We know that

$sin \: a = \frac{p}{h} = \frac{1}{2}$

And also,

$cos \: b = \frac{1}{2}$

$cos \: a \: = \frac{ \sqrt{3} }{2}$

$sin \: b \: = \frac{ \sqrt{3} }{2}$

$sin \: a \times \: cos \: \: b + cos \: a \: \times \: sin \: b$

$\frac{1}{2} \times \frac{1}{2} + \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{2}$

$\frac{1}{4} + \frac{3}{4}$

$= \frac{4}{4}$

$= 1$

$therefore \\ \: sin \: a \times cos \: b + cos \: a + sin \: b \: = 1$