1 + c o s 56 ∘ + c o s 58 ∘ − c o s 66 ∘ = Options: A . &nbsp 2 c o s 28 ∘ c o s 29 ∘ c o s 33 ∘ B . &nbsp 4 c o s 28 ∘ c o s 29 ∘ c o s 33 ∘ C . &nbsp 4 c o s 28 ∘ c o s 29 ∘ s i n 33 ∘ D . &nbsp 2 c o s 28 ∘ c o s 29 ∘ s i n 33 ∘

Answer: Option C : C 1 + c o s 56 ∘ + c o s 58 ∘ − c o s 66 ∘ = = 2 c o s 2 28 ∘ + 2 s i n 62 ∘ . s i n 4 ∘ = 2 c o s 2 28 ∘ + 2 c o s 28 ∘ . s i n 4 ∘ = 2 c o s 28 ∘ ( c o s 28 ∘ + c o s 86 ∘ ) = 2 c o s 28 ∘ .2 c o s 57 ∘ . c o s 29 ∘ = 4 c o s 28 ∘ c o s 29 ∘ s i n 33 ∘ Aliter: Apply the condition identify c o s A + c o s B − c o s C = − 1 + 4 c o s A 2 c o s B 2 s i n c 2 [ ∴ 56 ∘ + 58 ∘ + 66 ∘ = 180 ∘ ] We get the value of required expression equal to 4 c o s 28 ∘ c o s 29 ∘ s i n 33 ∘ .

1+cos 56∘+cos 58∘−cos 66∘=

Discussion Forum : Trigonometric Functions

Question -

$1 + c o s 56^{\circ} + c o s 58^{\circ} - c o s 66^{\circ} =$

Options:

A .

2 c o s 28^{\circ} c o s 29^{\circ} c o s 33^{\circ}

B .

4 c o s 28^{\circ} c o s 29^{\circ} c o s 33^{\circ}

C .

4 c o s 28^{\circ} c o s 29^{\circ} s i n 33^{\circ}

D .

2 c o s 28^{\circ} c o s 29^{\circ} s i n 33^{\circ}

Answer: Option C
:
C

$1 + c o s 56^{\circ} + c o s 58^{\circ} - c o s 66^{\circ} =$
= $2 c o s^{2} 28^{\circ} + 2 s i n 62^{\circ} . s i n 4^{\circ}$
= $2 c o s^{2} 28^{\circ} + 2 c o s 28^{\circ} . s i n 4^{\circ}$
= $2 c o s 28^{\circ} (c o s 28^{\circ} + c o s 86^{\circ})$
= $2 c o s 28^{\circ} .2 c o s 57^{\circ} . c o s 29^{\circ}$
= $4 c o s 28^{\circ} c o s 29^{\circ} s i n 33^{\circ}$
Aliter: Apply the condition identify
$c o s A + c o s B - c o s C = - 1 + 4 c o s \frac{A}{2} c o s \frac{B}{2} s i n \frac{c}{2}$
$[∴ 56^{\circ} + 58^{\circ} + 66^{\circ} = 180^{\circ}]$
We get the value of required expression equal to $4 c o s 28^{\circ} c o s 29^{\circ} s i n 33^{\circ}$ .

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Discussion Forum : Trigonometric Functions

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