Question

23. In AABC right angled at B, if tan A= V3, then cos A cos C-sin A sin C = (a)-1 (b) 0 (c) 1 (d) v3/2
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Answer 1

Option a is the right answer of these question

Answer 2

Given :  ΔABC right angled at B  

tan A= √3

To Find : cos A cos C-sin A sin C

(a)-1 (b) 0 (c) 1 (d) √3/2

Solution:

cos A cos C-sin A sin C

Using identity cos(x + y) = cosxcosy - sinxsiny

= cos(A + C)

Sum of angles of a triangle is 180°

Hence A + C + B = 180°

=> A + C + 90° = 180°

=> A + C = 90°

cos 90°  = 0

Hence cos A cos C-sin A sin C  = 0

or using A + C = 90°

Hence A = 90° - C

cosA = cos( 90° - C)

=> cosA = sinC

similarly CosC = sinA

cos A cos C-sin A sin C

= sinCsinA - sin A sin C

= 0

Correct option is  b) 0

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