Question

Consider the following statements:
(1) The value of $\cos {46}^o-\sin {46}^o$ is positive.
(2) The value of $\cos {44}^o-\sin {44}^o$ is negative
Which of the above statements is/are correct?

• A. (1) only
• B. (2) only
• C. Both (1) and (2)
• D. Neither (1) and (2)

Answer 1

Answer: (D)

Neither (1) and (2)

cosine function decreases from $0$ to ${90}^o$ and sin function increases from $0$ to ${90}^o$.
$\cos$ and $\sin$ function are equal at ${45}^o$
$\cos {46}^o<\sin {46}^o\Rightarrow \cos {46}^o-\sin {46}^o<0$

Similarly, $\cos {44}^o>\sin {44}^o$

$\Rightarrow \cos {44}^o-\sin {44}^o>0$
Option D is correct