(A) We know that $\sin(90^{\circ} - \theta) = \cos \theta$. Given expression: $\sin^{2} 51^{\circ} + \sin^{2} 39^{\circ}$. We can write $39^{\circ}$ a

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(A) We know that $\sin(90^{\circ} - \theta) = \cos \theta$. Given expression: $\sin^{2} 51^{\circ} + \sin^{2} 39^{\circ}$. We can write $39^{\circ}$ as $(90^{\circ} - 51^{\circ})$. So,$\sin^{2} 39^{\circ} = \sin^{2}(90^{\circ} - 51^{\circ}) = \cos^{2} 51^{\circ}$. Substituting this into the expression: $\sin^{2} 51^{\circ} + \cos^{2} 51^{\circ}$. Using the identity $\sin^{2} \theta + \cos^{2} \theta = 1$,we get $1$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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The value of $\sin^{2} 51^{\circ} + \sin^{2} 39^{\circ}$ is

KCET 2020 All KCET

A
$1$
B
$0$
C
$\sin 12^{\circ}$
D
$\cos 12^{\circ}$

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Trigonometrical Ratios, Functions and Identities

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Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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