the value of sin square 18+sin square72
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sin2 72 + sin2 18
we know sin 90 - theta = cos theta
and here theta is 18
so sin2 (90 - 18 ) = cos 2 72
so
sin2 72 + cos2 72 = 1
cuz of formula
sin2 theta + cos2 theta =1
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The value of sin²18+sin²72 is 1.
Given,
A trigonometric expression sin²18+sin²72.
To Find,
The value of this trigonometric expression.
Solution,
The given trigonometric expression is
sin²18+sin²72
Using the formula
sin(90-θ) = cosθ
Now,
sin(90-72) = cos 72
Similarly, sin²(90-72) = cos²(72)
sin²18 = cos²72
Substituting the value in the given expression
cos²72+sin²72
Using the identity, sin²θ+cos²θ = 1
So,
cos²72+sin²72 = 1
Hence, the value of sin²18+sin²72 is 1.
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