The correct option is A 0 (A) #160; #160; Given Expression=cos (270^∘ 15^∘)+sin(180^∘ 15^∘)= sin #160;15^∘+sin #160;15^∘=0 ...

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Sign of Trigonometric Ratios in Different Quadrants

cos 255∘+sin ...

Question

$cos 255^{\circ} + sin 165^{\circ} =$

0

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

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

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

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Solution

The correct option is A $0$
(A) $G i v e n E x p r e s s i o n = c o s (270^{\circ} - 15^{\circ}) + s i n (180^{\circ} - 15^{\circ}) = - s i n 15^{\circ} + s i n 15^{\circ} = 0$

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∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & - 2 0 & 0 & - 1 3 & - 5 & - 0 \end{matrix} ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ \begin{matrix} 3 & - 4 & 5 1 & 1 & - 2 2 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣

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I. The centroid of the triangle formed by $(2, 3, - 1), (5, 6, 3), (2, - 3, 1)$ is	a) $(2, 2, 2)$
II. The circumcentre of the triangle formed by $(1, 2, 3), (2, 3, 1), (3, 1, 2)$ is	b) $(3, 1, 4)$
III. The orthocenter of the triangle formed by $(2, 1, 5), (3, 2, 3), (4, 0, 4)$ is	c) $(1, 1, 0)$
IV. The incentre of the triangle formed by $(0, 0, 0), (3, 0, 0), (0, 4, 0)$ is	d) $(3, 2, 1)$
	e) $(0, 0, 0)$

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