Question

the value of sin square 15 + sin square 25 + sin square 65 + sin square 75​

Answer 1

Answer:

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Answer 2

$\sin^215$° + $\sin^225$° + $\sin^265$° + $\sin^275$° = 2

Step-by-step explanation:

We have,

$\sin^215$° + $\sin^225$° + $\sin^265$° + $\sin^275$°

To find, $\sin^215$° + $\sin^225$° + $\sin^265$° + $\sin^275$° = ?

∴ $\sin^215$° + $\sin^225$° + $\sin^265$° + $\sin^275$°

= $\sin^215$° + $\sin^225$° + $\sin^2(90-25)$ + $\sin^2(90-15)$

Using the trigonometric identity,

$\cos A$ = $\sin(90-A)$

= $\sin^215$° + $\sin^225$° + $\cos^225$° + $\cos^215$°

= ($\sin^215$° + $\cos^215$°) + ($\sin^225$° + $\cos^225$° )

Using the trigonometric identity,

$\sin^2A$ + $\cos^2 A$ = 1

= 1 + 1

= 2

∴ $\sin^215$° + $\sin^225$° + $\sin^265$° + $\sin^275$° = 2