Q)   If sin A = y, then express cos A and tan A in terms of y.

PYQ: Q 23(b) – CBSE 2025 – Code 30 – Series 5 – Set 1

Ans:  Given that sin A = y.

[Approach: Now, if we need to find cos A in terms of y and once we find cos A, then tan A will be easy. Let’s start by defining cos A in terms of y.]

Step 1: By Pythagoras theorem, we know that: sin² A + cos² A = 1

∵ it is given sin A = y, we substitute the same in the above equation, we get:

∴ y² + cos² A = 1

∴ cos² A = 1 – y²

Taking the square root of both sides, we get:

∴ cos A = ± √(1 – y²)

Step 2: Here we get 2 values i.e. both positive and negative roots.

If it is not specified in the question, we will consider only the positive root and solve:

∴ cos A = √(1 – y²)

Step 3:

Since, tan A is defined as: tan A = sin A / cos A

Now we have sin A = y and cos A = √(1 – y²):

Substituting these values in the above equation, we get:

∴ tan A = y / √(1 – y²)

[Note: if you take 2 values of cosine A, then 2 values of tan A need to be shown].

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