Question

Which among the following ratios, is not opposite of each other? (a) sinA and cosA. (b) cosA and secA. (c) tanA and cotA. d) CosecA and sinA​

Answer 1

Step-by-step explanation:

The theorem is that the ratio of the areas of two similar triangles is equal to the square of the ratio of the corresponding side

Answer 2

Step-by-step explanation:

Given:

(a) sinA and cosA

(b) cosA and secA

(c) tanA and cotA

d) cosecA and sinA

To find: Which among the following ratios, is not opposite of each other?

Solution:

We know that, there are six trigonometric ratios.

$\sin( \theta),\: \cos(\theta) ,\: \tan(\theta),\: \cot(\theta),\: \sec(\theta) ,\: \csc( \theta )$

and there are reciprocal/opposite to other three.

These pairs are

$\sin(\theta) ,\:\cosec(\theta) \\ \\ \cos(\theta) ,\:\sec(\theta) \\ \\ \tan(\theta) ,\:\cot( \theta)$

here,

On observing the given options, it is clear that, the following are opposite pairs.

(b) cosA and secA

(c) tanA and cotA

(d) cosecA and sinA

Thus,

Option (a)sinA and cosA are not opposite pair, it is actually complementary pair.

Final answer:

(a) sinA and cosA, following ratios, is not opposite of each other.

Hope it helps you.

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