First slide

Trigonometric Identities

Question

If the quadratic equation whole roots are $\cos e c^{2} θ, s e c^{2} θ$ is $x^{2} - λ x + λ = 0$ then

Moderate

A

$λ > 4$
B

$λ < 4$
C

$λ \geq 4$
D

$λ \leq 4$

Solution

$\begin{array}{l} s u m o f t h e r o o t s = λ = \sec^{2} θ + \csc^{2} θ = \frac{1}{\cos^{2} θ} + \frac{1}{\sin^{2} θ} \\ = \frac{\sin^{2} θ + \cos^{2} θ}{\sin^{2} θ \cos^{2} θ} \\ = \frac{1}{\sin^{2} θ \cos^{2} θ} \\ = \frac{4}{\sin^{2} 2 θ} \geq 4 \\ A l s o p r o d u c t o f t h e r o o t s = \csc^{2} θ \cdot \sec^{2} θ = \frac{1}{\sin^{2} θ \cos^{2} θ} \geq 4 \end{array}$
$∴$ The required equation is $x^{2} - t x + t = 0 w h e r e t \geq 4$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App