Question

find the value of sin²pie/4 +sin²3pie/4 + sin²5pie/4 +sin²7pie/4​

Answer 1

Step-by-step explanation:

Let pi/4=A

Sin^2A+sin^2 3A+sin^2 5A+sin^2 7A

We know that sin^2x=(1-cos 2x)/2

=1/2[(1-cos 2A)+(1-cos6A)+(1-cos10A)+(1-cos14A)]

=1/2[4-(cos 14A+cos 2A)-(cos 10A+cos 6A)]

=1/2[4–2cos 8A cos6A-2cos 8A cos 2A]

=2- cos 8A( cos 6A+ cos 2 A)

=2- cos 8A ( 2cos 4A.cos 2A) put A=pi/4 i,e 45 degree.

=2–2×cos 2pi×cos pi×cos pi/2 we know cos pi/2=0

=2–2×cos 2pi×cospi×0

=2–0

=2 answer

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Answer 2

Answer:

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Step-by-step explanation:

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