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Given tan(θ) = 8/6

In a right angled triangle, to the given angle ‘θ’ -> tan(θ) = (opposite side)/ (adjacent side)

This means the given ratio (opposite side)/ (adjacent side) = 8/6.

So let the opposite side = 8x and adjacent side = 6x

Then according to Pythagorean theorem, (hypotenuse) = √[(8x)

This gives the hypotenuse = 10x

Since cos(θ) = (adjacent side)/ (hypotenuse)->cos(θ) = 6x/10x.

Therefore cos(θ) = 6/10

Given tan(θ) = 3/4

In a right angled triangle, to the given angle ‘θ’ -> tan(θ) = (opposite side)/ (adjacent side)

This means the given ratio (opposite side)/ (adjacent side) = 3/4

So let the opposite side = 3x and adjacent side = 4x

Then according to Pythagorean theorem, (hypotenuse) = √[(3x)

This gives the hypotenuse = 5x

Since sin(θ) = ( opposite side)/ (hypotenuse)-> sin(θ) = 3x/5x

Thereforesin(θ) = 3/5