Question

If tan A=1root 3 and tan B=root 3 then find sin A Cos B (A, B<90)

Answer 1

Answer- The above question is from the chapter 'Introduction to Trigonometry'.

Trigonometry- The branch of Mathematics which helps in dealing with measure of three sides of a right-angled triangle is called Trigonometry.

Trigonometric Ratios:

sin θ  = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

cosec θ = Hypotenuse/Perpendicular

sec θ = Hypotenuse/Base

cot θ = Base/Perpendicular

Also, tan θ = sin θ/cos θ and cot θ = cos θ/sinθ

Trigonometric Identites:

1. sin²θ + cos²θ = 1

2. sec²θ - tan²θ = 1

3. cosec²θ - cot²θ = 1

Trigonometric Values of Angles from 0° to 90°:

(The table has been attached.)

Given question: If tan A = 1/√3 and tan B = √3, then find sin A cos B where (A < 90° > B).

Solution: tan A = 1/√3

tan A = tan 30°

⇒ A = 30°

tan B = √3

tan B = tan 60°

⇒ B = 60°

sin A cos B = sin 30° × cos 60°

                   = 1/2 × √3/2

                   =  √3/4

∴ Value of sin A cos B = √3/4