Question

1
In a triangle ABC ,right angled at C , if tan A= 1 \ √3 , Find the value of sin A - cos B +cos A . sin B .

Answer 1

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tanA=31

ACBC=31

AC=3BC

Also, (AC)2+(BC)2=(AB)2

3(BC)2+(BC)2=(AB)2

AB=2BC

AB:BC:AC=2:1:3

sinA=ABBC=21 cosA=ABAC=23

sinB=ABAC=23   

Answer 2

3/4

using pythagoras first calculate the side AB ( HYPOTENUSE)

now through observation we know sinA = 1/2

cosB = 1/2

cosA= √3/2

sin B = √3/2

putting them according to the question we get

1/2-1/2 + √3/2.√3/2

= 3/4

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