Value of {cos135^{∘}sin210^{∘}cos150^{∘}}{sin270^{∘}cos315^{∘}} is

Correct Answer is : 34{{3}}{4}43

Correct Answer is : 34{{3}}{4}43

Test Index

UPTET Paper 2 Math and Science 2019 Solved Paper

Question : 113 of 120

Marks: +1, -0

Value of

\frac{cos135^{∘}sin210^{∘}cos150^{∘}}{sin270^{∘}cos315^{∘}}

Solution:

Concept:

Use standard trigonometric values for standard angles and quadrant rules to find the value of each term.

Explanation:

First, reduce each angle to an acute angle using quadrant signs.

\cos 135^\circ = \cos(180^\circ - 45^\circ) = -\cos 45^\circ = -\frac{1}{\sqrt{2}}

\sin 210^\circ = \sin(180^\circ + 30^\circ) = -\sin 30^\circ = -\frac12

\cos 150^\circ = \cos(180^\circ - 30^\circ) = -\cos 30^\circ = -\frac{\sqrt{3}}{2}

\sin 270^\circ = -1

\cos 315^\circ = \cos(360^\circ - 45^\circ) = \cos 45^\circ = \frac{1}{\sqrt{2}}

Now substitute into the expression:

\frac{(-\frac{1}{\sqrt{2}})(-\frac12)(-\frac{\sqrt{3}}{2})}{(-1)(\frac{1}{\sqrt{2}})}

Numerator:

-\frac{\sqrt{3}}{4\sqrt{2}}

Denominator:

-\frac{1}{\sqrt{2}}

Dividing:

\frac{-\frac{\sqrt{3}}{4\sqrt{2}}}{-\frac{1}{\sqrt{2}}} = \frac{\sqrt{3}}{4}

Answer:

\frac{\sqrt{3}}{4}

(Option B)

Go to Question:

Prev Question

Next Question