Question

2sin 35°sin 25° - cos 10°=

Answer 1

Ответ:

Объяснение:

This expression can be simplified using trigonometric identities.

We know that:

sin(A - B) = sin A cos B - cos A sin B

Using this identity, we can rewrite the expression as:

2sin 35°sin 25° - cos 10° = 2sin(35° - 25°) - cos 10°

= 2sin 10° - cos 10°

= (2sin 10° - cos 10°) / (2sin 10° + cos 10°) * (2sin 10° + cos 10°) (Multiplying by the conjugate of the denominator to simplify)

= (2sin^2 10° - cos^2 10°) / (2sin 10° + cos 10°)

= (2(1 - cos^2 10°) - cos^2 10°) / (2sin 10° + cos 10°)

= (2 - 3cos^2 10°) / (2sin 10° + cos 10°)

So the simplified expression is (2 - 3cos^2 10°) / (2sin 10° + cos 10°).