# The Value of Sin 78° − Sin 66° − Sin 42° + Sin 60° is - Mathematics

MCQ
Sum

The value of sin 78° − sin 66° − sin 42° + sin 60° is

#### Options

• $\frac{1}{2}$

• $- \frac{1}{2}$

• −1

• None of these

#### Solution

None of these
$\sin78^\circ - \sin66^\circ - \sin42^\circ + \sin60^\circ$
$= \sin78^\circ - \sin42^\circ - \sin66^\circ + \sin60^\circ$
$= 2\sin\left( \frac{78^\circ - 42^\circ}{2} \right)\cos\left( \frac{78^\circ + 42}{2} \right) - \sin66^\circ + \sin60^\circ \left[ \because \sin A - \sin B = 2\sin\left( \frac{A - B}{2} \right)\cos\left( \frac{A + B}{2} \right) \right]$
$= 2\sin18^\circ \cos60^\circ - \sin66^\circ + \sin60^\circ$
$= 2 \times \frac{1}{2}\sin18^\circ - \sin66^\circ + \frac{\sqrt{3}}{2}$
$= \sin18^\circ - \sin66^\circ + \frac{\sqrt{3}}{2}$
$= \frac{\sqrt{5} - 1}{4} - 0 . 914 + \frac{\sqrt{3}}{2}$
$= 0 . 309 - 0 . 914 + 0 . 866$
$= 0 . 261$

Concept: Transformation Formulae
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 8 Transformation formulae
Q 5 | Page 21