Question

10. In triangle ABC, right angled at B, if tan A = 1 / √3, find the value of

(i) sin A cos C + cos A sin C (ii) cos A cos C – sin A sin C

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Answer 1

Answer:

(1) 1 (2) 0

Step-by-step explanation:

if tan a = 1/$\sqrt{3\\}$ then angle a = 30 degrees

sin a= sin 30= 1/2

cos a = cos 30= $\sqrt{3}$/2

and the sum of a triangle is 180 degree

one of the angle is 30 degree and another one is 90 degree so the third angle would be 180-90-30= 60 degree= angle c

so sin c = sin 60 degree = $\sqrt{3}$/2

cos c=cos 60= 1/2

put the values and u will get the answer

or a simpler method is :

in the first part sin a cos c+sin c cos a is asked which is sin (a+c)

and a+b+c=180(angle sum property)

b=90, a+c=180-90=90

sin(a+c)= sin (90)=1

and in the b part cos a cos c-sin a sin c is asked which is equal to cos(a+c)

and (a+c)= 90

cos(a+c) =cos 90=0