If sin x-y-1-2- sin x-y-3-2- and 0-y-x-90- find the value of x and y- respectively- A- 45- 15-B- 30- 45-C- 30- 45-D- 45- 60-

The correct option is A 45°, 15°sin (x nbsp; y) = 𝟏/𝟐⇒ x – y = 30°……….. (i) sin (x + y) = √𝟑/𝟐⇒ x + y = 60° ………..(ii) From equations (i) and (ii) 2x = 90° ...

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Byju's Answer

Standard IX

Mathematics

Trigonometric Ratio(sec,cosec,cot)

If sin x-y=1/...

Question

If $s i n (x - y) = \frac{1}{2}$ , $s i n (x + y) = \frac{\sqrt 3}{2}$ , and $0 < y < x < 90^{\circ}$ , find the value of x and y, respectively.

45°, 15°

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30°, 45°

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30°, 45°

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45°, 60°

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Solution

The correct option is A 45°, 15°
$s i n (x - y) = \frac{1}{2} \Rightarrow x - y = 30 °$ ……….. (i)
$s i n (x + y) = \frac{\sqrt 3}{2} \Rightarrow x + y = 60 °$ ………..(ii)
From equations (i) and (ii)
$2 x = 90 °$
$x = 45 °$
From equation (i)
$y = 45 ° - 30 ° = 15 °$

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If sin(x−y)=12 , sin(x+y)=√32, and0<y<x<90∘, find the value of x and y, respectively.

The correct option is A 45°, 15°sin(x−y)=12⇒x–y=30°……….. (i) sin(x+y)=√32⇒x+y=60° ………..(ii) From equations (i) and (ii) 2x=90° x=45° From equation (i) y=45°−30°=15°

If $s i n (x - y) = \frac{1}{2}$ , $s i n (x + y) = \frac{\sqrt 3}{2}$ , and $0 < y < x < 90^{\circ}$ , find the value of x and y, respectively.

The correct option is A 45°, 15°
$s i n (x - y) = \frac{1}{2} \Rightarrow x - y = 30 °$ ……….. (i)
$s i n (x + y) = \frac{\sqrt 3}{2} \Rightarrow x + y = 60 °$ ………..(ii)
From equations (i) and (ii)
$2 x = 90 °$
$x = 45 °$
From equation (i)
$y = 45 ° - 30 ° = 15 °$