Question

Statement-I : If and then

Statement-II : If sinA = sinB and cosA = cosB, then

- Statement-I is True, Statement-II is True; Statement-II is a correct explanation for Statement-I.
- Statement-I is True, Statement-II is True; Statement-II is NOT a correct explanation for Statement-I
- Statement-I is True, Statement-II is False
- Statement-I is False, Statement-II is True

Hint:

### In this question, given two statements. It is like assertion and reason. Statement1 is assertion and statement 2 is reason, Find the statement 1 is correct or not and the statement 2 correct or not if correct then is its correct explanation.

## The correct answer is: Statement-I is True, Statement-II is False

### Here, we have to find the which statement is correct and if its correct explanation or not.

Firstly,

Statement-I: and then

......(i)

..............(ii)

dividing (i) by (ii)

Again, sin A = sin B

(∴A= nπ ± B accordingly n is even or odd integer)

And cos A = cos B

⇒ A = nπ ± B (n ∈ I)

Therefore, statement-I is true,

Now,

Statement-II: sinA = sinB and cosA = cosB, then

Also, tanA = tanB

tanA − tanB = 0

tan(A−B) = 0

A−B=nπ

∴A=nπ+B (n∈I)

Therefore, Statement-II is also true and correct explanation of Statement-I.

Hence, the correct answer is Statement-I is true, Statement-II is true; Statement-II is NOT a correct explanation for Statement-I

In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, Start solving first Statement and try to prove it. Then solve the Statement-II.

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