Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesAddition, Multiplication, Subtraction formula based,Multiple/Submultiple anglesMedium2 minQB

MathematicsMediuminteger

If $tan α$ is an integral solution of $4 x^{2} - 16 x + 15 < 0$ and $cos β$ is the slope of the bisector of the angle in the first quadrant between the x and y axis. Then $sin (α + β) : sin (α - β) =$

Answer:

Solution:

$4 x^{2} - 16 x + 15 < 0$

$4 x^{2} - 10 x - 6 x + 15 < 0$

$2 x (2 x - 5) - 3 (2 x - 5) < 0$

$\frac{3}{2} < x < \frac{5}{2} \Rightarrow x = 2$

$tan α = 2; cos β = 1$

$\frac{s i n ( α + β )}{s i n ( α - β )} = \frac{t a n α + t a n β}{t a n α - t a n β} = \frac{2 + 0}{2 - 0} = 1$

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Addition, Multiplication, Subtraction formula based,Multiple/Submultiple angles

⏱ 2mℹ️ Source: QB

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