The value of $c o s 52^{\circ} + c o s 68^{\circ} + c o s 172^{\circ}$ is

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$\frac{3}{2}$

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Solution

The correct option is A
0

$c o s 52^{\circ} + c o s 68^{\circ} + c o s 172^{\circ} = 2 c o s (\frac{52^{\circ} + 68^{\circ}}{2}) c o s (\frac{52^{\circ} - 68^{\circ}}{2}) + c o s 172^{\circ} [∵ c o s A + c o s B = 2 c o s (\frac{A + B}{2}) c o s (\frac{A - B}{2})] = 2 c o s 60^{\circ} + c o s (- 8^{\circ}) + c o s 172^{\circ} = 2 \times \frac{1}{2} c o s 8^{\circ} + c o s 172^{\circ} = c o s 8^{\circ} + c o s 172^{\circ} = 2 c o s (\frac{8^{\circ} + 172^{\circ}}{2}) c o s (\frac{8^{\circ} - 172^{\circ}}{2}) = 2 c o s 90^{\circ} c o s 82^{\circ} = 0$

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Similar questions

Q. The value of cos 52° + cos 68° + cos 172° is
(a) 0
(b) 1
(c) 2
(d) 3/2

Q. The value of

\frac{cos 58^{\circ}}{sin 32^{\circ}} + \frac{sin 22^{\circ}}{cos 68^{\circ}} - \frac{cos 38^{\circ} cosec 52^{\circ}}{tan 18^{\circ} tan 35^{\circ} tan 72^{\circ} tan 55^{\circ}}

Q. The value of

\frac{cos 62^{\circ}}{sin 52^{\circ} sin 66^{\circ}} + \frac{cos 52^{\circ}}{sin 66^{\circ} sin 62^{\circ}} + \frac{cos 66^{\circ}}{sin 62^{\circ} sin 52^{\circ}}

is equal to :

Q. The value of

t a n 48^{\circ} . t a n 23^{\circ} . t a n 42^{\circ} . t a n 67^{\circ}

and

c o s 38^{\circ} . c o s 52^{\circ} - s i n 38^{\circ} . s i n 52^{\circ}

is equal to

Evaluate the value of the following expression:

$A = \frac{cos 58^{\circ}}{sin 32^{\circ}} + \frac{sin 22^{\circ}}{cos 68^{\circ}} - \frac{cos 38^{\circ} c o s e c 52^{\circ}}{tan 18^{\circ} tan 72^{\circ}}$

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The value of cos52∘+cos68∘+cos172∘ is

The correct option is A 0 cos52∘+cos68∘+cos172∘=2cos(52∘+68∘2)cos(52∘−68∘2)+cos172∘[∵cosA+cosB=2cos(A+B2)cos(A−B2)]=2cos60∘+cos(−8∘)+cos172∘=2×12cos8∘+cos172∘=cos8∘+cos172∘=2cos(8∘+172∘2)cos(8∘−172∘2)=2cos90∘ cos82∘=0

The value of $c o s 52^{\circ} + c o s 68^{\circ} + c o s 172^{\circ}$ is