Question

Which trigonometric ratio will not have the same value as sin A?

Answer 1

$\sin\theta=\dfrac{opposite}{hypotenuse}\\\\\cos\theta=\dfrac{adjacent}{hypotenuse}\\\\\tan\theta=\dfrac{opposite}{adjacent}$

It's an isosceles triangle, therefore AB = BC.

Let AB = BC = x abd AC = y. Then:

$opposite=adjacent=x\\hypotenuse=y\\\\\sin A=\dfrac{x}{y}\\\\\cos A=\dfrac{x}{y}\\\\\sin C=\dfrac{x}{y}\\\\\cos C=\dfrac{x}{y}\\\\\tan C=\dfrac{x}{x}=1$

Answer: C. tan C

Answer 2

Answer:

correct option is d) cos C

Step-by-step explanation:

Since,

$SinФ = \frac{perpendicular}{hypotenuses}$

$CosФ = \frac{base}{hypotenuses}$

$TanФ = \frac{perpendicular}{base}$

In triangle ABC , sides are denoted as mention in figure-1

$sin A =\frac{x}{z}$

$cos A =\frac{y}{z}$

$sin C =\frac{y}{x}$

$tan C =\frac{y}{x}$

$cos C =\frac{x}{z}$

hence, cos C have similar value as sin A

Therefore, correct option is d) cos C