Question

$in \: a \: \triangle{abc} \angle{c} = 90 \: and \: \tan(a) = 1 by{ \sqrt{3} }. \\ find \: the \: values \: of - \\ \sin(a) \times \cos(b) + \cos(a) \times \sin(b)$
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Answer 1

Step-by-step explanation:

a/b × a/b + c/b ×c/b

a^2 /b^2 + c^2/b^2 =

a^2+c^2 / b^2 =

b^2 /b^2 = 1

answer is 1

hope its help u......

Answer 2

$\huge \underline \textbf{answer - }$

Consider a $\triangle{abc}$in which $\angle{c} = 90$and tan A=1/

$\sqrt{3}$

Then tan A =1/$\sqrt{3}$

=>BC/AC =1/3

Let BC =x. Then AC =$\sqrt{3x}$

By Pythagoras theorem,

AB²=BC² +AC²

=>AB² =

$( \sqrt{3x} )^2+ x2 = (3^2 ²+ x^2 ) = 4x^2$

=>AB² =$( \sqrt{4x} )2 = 2x$

For T-ratios of $\angle{a}$

Base =AC=$\sqrt{3x}$

Perpendicular =BC =x and hypotenuse =AB=2x.

$\therefore \sin(a) =$BC/AB =x/2x=1/2 and

$\cos(a)$=AC/AB =$\sqrt{3x }/2$

For T-ratios of $\angle{b}$

Base =BC= x, hypotenuse =AB =2x

Perpendicular =$\sqrt{3x}$

$\therefore \sin(b) =$AC/AB =$\sqrt{3}/2$

And cos B =BC /AB =x /2x =1/2.

$( \sin a \times \cos b + \cos a \times \sin b ) =$

1/2 *1/2+$\sqrt{3} /2*sqrt3/2$

=(1/4 +1/4)=1