Evaluate sin 2-4-sin 23 -4-sin 25 -4-sin 27 -4-

The correct option is D 2We have ( sin^2 ( π/4 )+sin^2 ( 7π/4 ) )+ ( sin^2 ( 3π/4 )+sin^2 ( 5π/4 ) ) = ( sin^2 ( π/4 )+sin^2 ( 2π π/4 ) )+ ( sin^2 ( 3π/4 ...

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Byju's Answer

Standard X

Mathematics

Range of Trigonometric Ratios from 0 to 90 Degrees

Evaluate sin ...

Question

Evaluate $s i n^{2} (\frac{π}{4}) + s i n^{2} (\frac{3 π}{4}) + s i n^{2} (\frac{5 π}{4}) + s i n^{2} (\frac{7 π}{4})$ .

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Solution

The correct option is B 2
We have $(s i n^{2} (\frac{π}{4}) + s i n^{2} (\frac{7 π}{4})) + (s i n^{2} (\frac{3 π}{4}) + s i n^{2} (\frac{5 π}{4}))$

$= (s i n^{2} (\frac{π}{4}) + s i n^{2} (2 π - \frac{π}{4})) + (s i n^{2} (\frac{3 π}{4}) + s i n^{2} (2 π - \frac{3 π}{4}))$

$= (s i n^{2} (\frac{π}{4}) + c o s^{2} (\frac{π}{4})) + (s i n^{2} (\frac{3 π}{4}) + c o s^{2} (\frac{3 π}{4})) = 2$

Suggest Corrections

Evaluate sin2(π4)+sin2(3π4)+sin2(5π4)+sin2(7π4).

The correct option is B 2We have (sin2(π4)+sin2(7π4))+(sin2(3π4)+sin2(5π4)) =(sin2(π4)+sin2(2π−π4))+(sin2(3π4)+sin2(2π−3π4)) =(sin2(π4)+cos2(π4))+(sin2(3π4)+cos2(3π4))=2

Evaluate $s i n^{2} (\frac{π}{4}) + s i n^{2} (\frac{3 π}{4}) + s i n^{2} (\frac{5 π}{4}) + s i n^{2} (\frac{7 π}{4})$ .