The equality 32x-5-3csc2x is satisfied by

The correct option is B no value of x Given, 3 ^ 2 x =5 3 ^ 2 x #160; ⇒ 3cos ^ 2 x=5 3sin ^ 2 x ⇒ 3(cos ^ 2 x+sin ^ 2 x)=5 But ...

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Standard XII

Mathematics

Trigonometric Equations

The equality ...

Question

The equality $\frac{3}{{sec}^{2} x} = 5 - \frac{3}{c s c^{2} x}$ is satisfied by

all values of

x

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exactly two values of

x

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only one value of

x

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no value of

x

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infinitely many but not all values of

x

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Solution

The correct option is B no value of $x$
Given, $\frac{3}{{sec}^{2} x} = 5 - \frac{3}{{csc}^{2} x}$
$\Rightarrow 3 {cos}^{2} x = 5 - 3 {sin}^{2} x$
$\Rightarrow 3 ({cos}^{2} x + {sin}^{2} x) = 5$
But it is not true because ${cos}^{2} x + {sin}^{2} x = 1$
Therefore, the correct option is $D$ .

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If the circles $x^{2} + y^{2} + 2 a x + c y + a = 0$ and $x^{2} + y^{2} - 3 a x + d y - 1 = 0$ interesect in two distinct points P and Q then the line 5x + by - a = 0 passes through P and Q for
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is satisfied by only one real value of

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The equality 3sec2x=5−3csc2x is satisfied by

The correct option is B no value of xGiven, 3sec2x=5−3csc2x⇒3cos2x=5−3sin2x⇒3(cos2x+sin2x)=5But it is not true because cos2x+sin2x=1Therefore, the correct option is D.

The equality $\frac{3}{{sec}^{2} x} = 5 - \frac{3}{c s c^{2} x}$ is satisfied by

The correct option is B no value of $x$
Given, $\frac{3}{{sec}^{2} x} = 5 - \frac{3}{{csc}^{2} x}$
$\Rightarrow 3 {cos}^{2} x = 5 - 3 {sin}^{2} x$
$\Rightarrow 3 ({cos}^{2} x + {sin}^{2} x) = 5$
But it is not true because ${cos}^{2} x + {sin}^{2} x = 1$
Therefore, the correct option is $D$ .