(B) Given $0 < \theta < \frac{\pi}{2}$ and $\sin \theta \cos \theta = \frac{12}{25}$.We need to find $\sin^4 \theta + \cos^4 \theta$.Using the identit

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(B) Given $0 We need to find $\sin^4 \theta + \cos^4 \theta$.Using the identity $a^2 + b^2 = (a + b)^2 - 2ab$,we have:$\sin^4 \theta + \cos^4 \theta = (\sin^2 \theta)^2 + (\cos^2 \theta)^2$$= (\sin^2 \theta + \cos^2 \theta)^2 - 2 \sin^2 \theta \cos^2 \theta$Since $\sin^2 \theta + \cos^2 \theta = 1$,we get:$= (1)^2 - 2(\sin \theta \cos \theta)^2$$= 1 - 2 \left(\frac{12}{25}\right)^2$$= 1 - 2 \left(\frac{144}{625}\right)$$= 1 - \frac{288}{625}$$= \frac{625 - 288}{625} = \frac{337}{625}$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Mix Examples-Trigonometrical Ratios, Functions and Identities

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If $0 < \theta < \frac{\pi}{2}$ and $\sin \theta \cos \theta = \frac{12}{25}$,then $\sin^4 \theta + \cos^4 \theta$ is equal to

AP EAMCET 2021 All AP EAMCET

A
$\frac{327}{625}$
B
$\frac{337}{625}$
C
$\frac{347}{625}$
D
$\frac{340}{625}$

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Trigonometrical Ratios, Functions and Identities

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Mix Examples-Trigonometrical Ratios, Functions and Identities

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