CBSE (Science) Class 11CBSE
Share

# Reduce Each of the Following Expressions to the Sine and Cosine of a Single Expression: Cos X − Sin X - CBSE (Science) Class 11 - Mathematics

ConceptTrigonometric Functions of Sum and Difference of Two Angles

#### Question

Reduce each of the following expressions to the sine and cosine of a single expression:

cos x − sin

#### Solution

$\text{ Let } f\left( x \right) = \cos x - \sin x$
$\text{ Dividing and multiplying by } \sqrt{1^2 + 1^2}, i . e . \text{ by }\sqrt{2,} \text{ we get } :$
$f\left( x \right) = \sqrt{2}\left( \frac{1}{\sqrt{2}}\cos x - \frac{1}{\sqrt{2}}\sin x \right)$
$\Rightarrow f\left( x \right) = \sqrt{2}(\cos45°\cos x - \sin45°\sin x)$
$\Rightarrow f\left( x \right) = \sqrt{2}\cos\left( \frac{\pi}{4} + x \right)$
$\text{ Again },$
$f\left( x \right) = \sqrt{2}\left( \frac{1}{\sqrt{2}}\cos x - \frac{1}{\sqrt{2}}\sin x \right)$
$\Rightarrow f\left( x \right) = \sqrt{2}(\sin45°\cos x - \cos45∏\sin x)$
$\Rightarrow f(x) = \sqrt{2} \sin\left( \frac{\pi}{4} - x \right)$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for Mathematics Class 11 (2019 to Current)
Chapter 7: Values of Trigonometric function at sum or difference of angles
Ex.7.20 | Q: 2.2 | Page no. 26

#### Video TutorialsVIEW ALL [1]

Solution Reduce Each of the Following Expressions to the Sine and Cosine of a Single Expression: Cos X − Sin X Concept: Trigonometric Functions of Sum and Difference of Two Angles.
S