prove that sin square 25 degree + sin square 65 degree is equal to 1
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Answered by
19
Solution:
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We know that,
i ) sin(90-A) = cosA
ii) sin²A + cos²A =1
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Now ,
sin²25 + sin²65
= sin² 25 + sin² (90-25)
= sin² 25°+ cos² 25
= 1
••••
Answered by
4
Consider the provided information.
\sin^2A\cos^2B-\cos^2A\sin^2B=\sin^2A-\sin^2B
Consider the LHS.
\sin^2A\cos^2B-\cos^2A\sin^2B
\sin^2A(1-\sin^2B)-(1-\sin^2A)\sin^2B (∴\cos^2x=1-\sin^2x)
\sin^2A-\sin^2A\sin^2B-\sin^2B+\sin^2A\sin^2B
\sin^2A-\sin^2B
Hence, proved.
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