Q. 94.2( 207 Votes )

In triangle ABC, right-angled at B, if find the value of:

(i) Sin A Cos C + Cos A Sin C

(ii) Cos A Cos C – Sin A Sin C

Answer :


For finding value of sin A cos C + cos A sin C , we need to find values of sin A, cos C, cos A, sin C

tan A = =

If BC is k, then AB will be, where k is a positive integer

In ΔABC,

AC2 = AB2 + BC2

      = ()2 + (k)2

      = 3k2 + k2 = 4k2

    AC = 2k
For finding the perpendicular and base for an angle of a right angled triangle, always take the side opposite to the angle as perpendicular and the other side as base

We know that,

Now, for angle A, Perpendicular will be side opposite to angle A that is BC and Hypotenuse will be AC

Sin A =


= =


And also by cosine formula, 

For angle A, base will be AB and hypotenuse will be AC

Cos A =


= =



For angle C, Perpendicular will be AB and hypotenuse will be AC

Sin C =


= =



For angle C, base will be equal to BC and hypotenuse equal to AC

Cos C =


= =


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


=


=


=


(ii) cos A cos C - sin A sin C


= () () – () ()


=


= 0

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