In ∆ABC Right Angled At B, If Tan A= √3, Then Cos A Cos C- Sin A Sin C - Bzziii.com

In ∆ABC right angled at B, if tan A= √3, then cos A cos C- sin A sin C =

(a) -1 

(b) 0 

(c) 1 

(d) `√3/2`

(b) 0 

Explanation:

Given,

tan A= √3     `\angle`A= `60^{0}`

In, △ ABC

Angle Sum Property

 `\angle`A +  `\angle`B +  `\angle`C =  `180^{0}`

 `60^{0}`  +  `90^{0}` +  `\angle`C =  `180^{0}`

`150^{0}` +  `\angle`C =  `180^{0}`

 `\angle`C =  `180^{0}` - `150^{0}`

 `\angle`C =  `30^{0}`

Now,

 cos A cos C = sin A sin C

=  cos `60^{0}` cos `30^{0}` = sin `60^{0}` sin `30^{0}`

= `frac{1}{2}` x `\frac{\sqrt{3}}{2}` - `\frac{\sqrt{3}}{2}` x `frac{1}{2}` 

= 0

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CBSE Class 10 Mathematics Sample Paper-2022