Question

IN TRAINGLE ABC ,RIGHT ANGLED AT B ,IF TAN A =1 /ROOT3,FIND THE VALUE OF

I)SIN A COS C + COS A SIN C .

PLEASE ANSWER ME FRENDS ...............^ . ^

Answer 1

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

a=30°

c=60°

sinA cosC +cosA sinC

=sin( A+C)

=sin=90

=1

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ɦσρε เƭ ɦεℓρร ყσµ 

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Answer 2

Solution:

It is given that In triangle ABC,Right-angled at B if tan A =1/√3.

•°• We have right-angled Triangle ABC in which tan A = 1/√3

☛ { From Given Attachment } ☛

Given, tan A = 1/√3 = BC/AB

________________________________

Let Side BC measure be k .

So, Side AB measure = √3k

•°• Using Pythagoras theorem , We have

By Pythagoras theorem, In ∆ABC ;

☛ H² = P² + B²

☛ Ac² = AB² + BC²

☛ AC² = (√3k)² + (k)²

☛ AC² = 3k² + k²

☛ AC² = 4k²

•°• ☛ AC = 2k

Now, on comparing Values of Trigonometric Ratio, We have ;

(I) Sin A = BC/AC =k/2k = ½

(ii) Cos C = BC/AC =k/2k = ½

(III) CoS A = AB/AC = √3k/2k = √3/2

(Iv) Sin A = AB/AC = √3k/2k =√3/2

Now, We have to find the value of ;i)SIN A COS C + COS A SIN C .

☛ ½ * ½ + √3/2 *√3/2

☛ 1/4 + 3/4

☛ 4/4

☛ 1

Therefore, Value of SIN A COS C + COS A SIN C is 1.