First slide

Trigonometric Identities

Question

If $15 \sin^{4} x + 10 \cos^{4} x = 6$ , Then $t {an}^{2} x =$

Moderate

A

$\frac{1}{5}$
B

$\frac{2}{5}$
C

$\frac{2}{3}$
D

$\frac{1}{3}$

Solution

$15 \sin^{4} x + 10 \cos^{4} x = 6 {(\sin^{2} x + \cos^{2} x)}^{2}$
$\begin{array}{l} \Rightarrow 9 \sin^{4} x + 4 \cos^{4} x - 12 \sin^{2} x \cos^{2} x = 0 \\ \Rightarrow {(3 \sin^{2} x - 2 \cos^{2} x)}^{2} = 0 \\ \Rightarrow \tan^{2} x = 2 / 3 . \end{array}$

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