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Critical Point

Assertion :St...

Question

Assertion :Statement 1: $cos 1 < sin 1 (i n r a d i a n s)$ . Reason: Statement 2: Cosine x decreases but sine x increases for $x \in (0, \frac{π}{2})$

Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

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Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1.

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STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

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STATEMENT 1 is FALSE and STATEMENT 2 is TRUE.

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Solution

The correct option is B Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1.
We know that $cos x > sin x$ for $x \in [0, \frac{π}{4})$
and $cos x < sin x$ for $x \in (\frac{π}{4}, \frac{π}{2}]$
Since, $1 \in (\frac{π}{4}, \frac{π}{2})$

Therefore, $cos 1 < sin 1$

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Statement 2: x – a is a factor of the polynomial P(x).

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Statement $1 : (p \land \sim q) \land (\sim p \land q)$ is a fallacy.

Statement $2 : (p \Rightarrow q) \Leftrightarrow (\sim q \Rightarrow\sim p)$ is a tautology.

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1 :

x y + y z + z x = 1

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A B C

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