In un triangolo rettangolo l'ipotenusa è lunga 20 cm e fra gli angoli acuti \( \beta \) e \( \gamma \) vale la relazione \( \sin \beta=2 \sin \gamma \). Trova l'area del triangolo. \[ \left[80 \mathrm{~cm}^{2}\right] \]

JSTION 11 Prove the following identity: \( \frac{\cos ^{2}\left(90^{\circ}+\theta\right)}{\cos (-\theta)+\sin \left(90^{\circ}-\theta\right) \cos \theta}=\frac{1}{\cos \theta}-1 \) Determine the general solution of: \( \tan x \sin x+\cos x \tan x=0 \). Consider the following expression: \( 2 \sin ^{2} 3 x-\sin ^{2} x-\cos ^{2} x \) 11.3.1 Simplify the expression to a single trigonometric ratio of \( x \). 11.3.2 Write down the maximum value of the expression.

Дан треугольник \( A B C \), в котором известно, нто \( A B=B C . \angle A=15^{\circ} \). Найди внешний гол этого треугольника, который является межным для угла \( C \), ответ дай в градусах.

En un triángulo rectángulo, uno de los ángulos agudos mide 35 grados. ¿Cuál es el valor del otro ángulo agudo?

The value of \( \sec \left(300^{\circ}\right) \sin \left(270^{\circ}-\theta\right)+\tan \left(-45^{\circ}\right) \cos \left(360^{\circ}-\theta\right) \) is \( \begin{array}{llll}\text { (a) }-3 \sin \theta & \text { (b) }-3 \cos \theta & \text { (c) } 3 \cos \theta & \text { (d) } 0\end{array} \)

(6) The value of \( \sec \left(300^{\circ}\right) \sin \left(270^{\circ}-\theta\right)+\tan \left(-45^{\circ}\right) \cos (3 M-9) \) is \( \begin{array}{lll}\text { (a) }-3 \sin \theta & \text { (b) }-3 \cos \theta & \text { (c) } 3 \cos \theta\end{array} \) (7) If the product of two roots of the equation : \( (k-2) x^{2}-6 x+12=0 \) equals 3