secθsinθ is equivalent to:

Ans: tanθ?

sec A * sin A = 1/Cos A * sin A =

Sin A/Cos A = Tan A.

To justify whether secθsinθ is equivalent to tanθ, we need to remind ourselves of the definitions of those trigonometric functions.

The secant function (secθ) is defined as the reciprocal of the cosine function (cosθ). Mathematically, it can be represented as secθ = 1/cosθ.

The sine function (sinθ), on the other hand, represents the ratio of the length of the side opposite to an acute angle θ in a right triangle to the hypotenuse. It can be expressed as sinθ = opposite side / hypotenuse.

To figure out if secθsinθ equals tanθ, we can rewrite secθsinθ using the definitions of secθ and sinθ.

secθsinθ = (1/cosθ) * (opposite side / hypotenuse)

As we know from trigonometry, opposite side / hypotenuse is equal to sinθ.

secθsinθ = (1/cosθ) * sinθ

Now, let's simplify further by multiplying the two fractions:

secθsinθ = sinθ/cosθ

This expression is identical to the definition of the tangent function (tanθ), which is the ratio of sinθ to cosθ. Mathematically, it is expressed as tanθ = sinθ/cosθ.

Therefore, secθsinθ is indeed equivalent to tanθ.