Question

please solve it fast ...​

Answer 1

Answer:

Sin(x/2) = 0.99

Cos(x/2) = 0.126

Tan(x/2) = 7.86

Step-by-step explanation:

निम्नलिखित प्रत्येक प्रश्न में \sin \dfrac{x}{2}, \cos \dfrac{x}{2} तथा \tan \dfrac{x}{2} ज्ञात कीजिए: \sin x = \dfrac{1}{4}, x द्वितीय चतुर्थाश में है।

Sinx = 1/4

Sinx = 2Sin(x/2)Cos(x/2)

=> 2Sin(x/2)Cos(x/2) = 1/4

=> Sin(x/2)Cos(x/2) = 1/8

Squaring both sides

Sin²(x/2)Cos²(x/2) = 1/64

=> Sin²(x/2)(1 - Sin²(x/2)) = 1/64

Let say Sin(x/2) = y

then

y(1-y) = 1/64

=> y² - y + 1/64 = 0

=> 64y² - 64y + 1 = 0

=> y = (64 ± √(64² - 64*4) )/(2 *64)

=> y = (64 ± 16√15 )/(2 *64)

=> y = (64 ± 61.97)/128

y = 0.98 or 0.0159

Sin²(x/2) = 0.98 or 0.0159

Sin(x/2) = 0.99 or 0.126

as Sinx = 1/4 is in

Sin(x/2) = 0.99 Cos(x/2) = 0.126

Tan(x/2) = 0.99/0.126 = 7.86

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