$\cos 45 ° . \sec 45 ° =$

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$\sin 60 ° . \cos e c 60 °$

$\sin 45 ° . \cos e c 45 °$

answer is A, B, C.

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Detailed Solution

Let's begin with the given expression: cos 45° × sec 45°.

Step-by-Step Solution:

We know that the cosine of 45° is:
cos 45° = 1 / √2
Similarly, secant is the reciprocal of cosine. Hence:
sec 45° = 1 / cos 45° = √2
Now, substituting these values into the given expression:
cos 45° × sec 45° = (1 / √2) × √2
On simplifying, the result is:
cos 45° × sec 45° = 1

Additional Examples

Example 1: sin 45° × cos 45°

We know that sin 45° = cos 45° = 1 / √2.

So, the expression sin 45° × cos 45° is: sin 45° × cos 45° = (1 / √2) × (1 / √2) = 1/2.

Example 2: sin 60° × sec 60°

We know that sin 60° = √3 / 2 and sec 60° = 2 / √3.

The expression sin 60° × sec 60° is: sin 60° × sec 60° = (√3 / 2) × (2 / √3) = 1.

Conclusion

In this example, cos 45° × sec 45° evaluates to 1. Understanding the relationship between cosine and secant helps simplify such calculations easily. Keep practicing similar problems to gain more clarity on trigonometric functions and their properties!

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