KCET · Maths · Complex Number
The value of \(\sin ^{2} 51^{\circ}+\sin ^{2} 39^{\circ}\) is
- A 1
- B 0
- C \(\sin 12^{\circ}\)
- D \(\cos 12^{\circ}\)
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
We have,
\(\begin{aligned}
&\sin ^{2} 51^{\circ}+\sin ^{2} 39^{\circ} \\
&\sin ^{2} 51^{\circ}+\sin ^{2}\left(90^{\circ}-51^{\circ}\right) \\
&\sin ^{2} 51^{\circ}+\cos ^{2} 51^{\circ}=1
\end{aligned}\)
\(\begin{aligned}
&\sin ^{2} 51^{\circ}+\sin ^{2} 39^{\circ} \\
&\sin ^{2} 51^{\circ}+\sin ^{2}\left(90^{\circ}-51^{\circ}\right) \\
&\sin ^{2} 51^{\circ}+\cos ^{2} 51^{\circ}=1
\end{aligned}\)
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