c o s 2 48 ∘ − s i n 2 12 ∘ = Options: A . &nbsp √ 5 − 1 4 B . &nbsp √ 5 + 1 8 C . &nbsp √ 3 − 1 4 D . &nbsp √ 3 + 1 2 √ 2

Answer: Option B : B c o s 2 A − s i n 2 B = cos(A + B). Cos(A - B) ∴ c o s 2 48 ∘ − s i n 2 12 ∘ = c o s 60 ∘ . c o s 36 ∘ = 1 2 ( √ 5 + 1 4 ) = √ 5 + 1 8

cos248∘−sin212∘=

Discussion Forum : Trigonometric Functions

Question -

$c o s^{2} 48^{\circ} - s i n^{2} 12^{\circ} =$

Options:

A .

\frac{\sqrt{5} - 1}{4}

B .

\frac{\sqrt{5} + 1}{8}

C .

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

D .

\frac{\sqrt{3} + 1}{2 \sqrt{2}}

Answer: Option B
:
B

$c o s^{2} A - s i n^{2} B$ = cos(A + B). Cos(A - B)

$∴ c o s^{2} 48^{\circ} - s i n^{2} 12^{\circ} = c o s 60^{\circ} . c o s 36^{\circ}$

= $\frac{1}{2} (\frac{\sqrt{5} + 1}{4}) = \frac{\sqrt{5} + 1}{8}$

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Discussion Forum : Trigonometric Functions

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