10 клас. Алгебра. Урок 31. Основні співвідношення між тригонометричними функціями одного аргументу

1) $1-\cos^2\alpha;$

7) $\frac{1}{\cos^2\alpha}-1;$

2) $\sin^2\beta-1;$

8) $1-\sin^2\alpha+\ctg^2\alpha\sin^2\alpha;$

3) $\sin^2\phi+\cos^2\phi+1;$

9) $\cos^2\alpha+\ctg^2\alpha-\frac{1}{\sin^2\alpha};$

4) $1-\sin^23\alpha-\cos^23\alpha;$

10) $\frac{\sin^2\beta}{1-\sin^2\beta}\cdot\ctg^2\alpha;$

5) $\frac{1-\sin^2\alpha}{1-\cos^2\alpha};$

11) $\left(1+\sin\frac{x}{2}\right)\left(1-\sin\frac{x}{2}\right);$

6) $\cos\alpha\tg\alpha;$

12) $\left(\sin\alpha+\cos\alpha\right)^2+\left(\sin\alpha-\cos\alpha\right)^2.$

1) $\left(1+\tg\alpha\right)^2+\left(1-\tg\alpha\right)^2;$

8) $\frac{\tg3\alpha}{\tg^23\alpha-1}\cdot\frac{1-\ctg^23\alpha}{\ctg3\alpha};$

2) $\sin^4\alpha+2\sin^2\alpha\cos^2\alpha+\cos^4\alpha;$

9) $\frac{\ctg\alpha}{\tg\alpha+\ctg\alpha};$

3) $\frac{\sin\alpha}{1+\cos\alpha}+\frac{\sin\alpha}{1-\cos\alpha};$

10) $\frac{1-\ctg\gamma}{1-\tg\gamma};$

4) $\ctg x+\frac{\sin x}{1+\cos x};$

11) $\cos^4\alpha-\cos^2\alpha+\sin^2\alpha;$

5) $\frac{1-\sin x}{\cos x}-\frac{\cos x}{1+\sin x};$

12) $\sin^4\alpha+\sin^2\alpha\cos^2\alpha+\cos^2\alpha;$

6) $\frac{\sin\alpha}{1+\cos\alpha}+\frac{1+\cos\alpha}{\sin\alpha};$

13) $\cos\left(-\alpha\right)+\cos\alpha\tg^2\left(-\alpha\right);$

7) $\frac{\tg\alpha+\tg\beta}{\ctg\alpha+\ctg\beta};$

14) $\frac{1+\sin\left(-\beta\right)}{\cos\left(-\beta\right)}-\tg\left(-\beta\right).$

1) $\frac{\cos^3\alpha-\sin^3\alpha}{1+\sin\alpha\cos\alpha}=\cos\alpha-\sin\alpha;$

5) $\frac{\ctg^2\alpha-\cos^2\alpha}{\sin^2-\tg^2\alpha}=-\ctg^2\alpha;$

2) $\cos^2\alpha+2\sin^2\alpha+\sin^2\alpha\tg^2\alpha=\frac{1}{\cos^2\alpha};$

6) $\frac{\sin\alpha+\tg\alpha}{1+\cos\alpha}=\tg\alpha;$

3) $\tg^2\alpha-\sin^2\alpha=\tg^2\alpha\sin^2\alpha;$

7) $1+\left(\ctg^2\alpha-\tg^2\alpha\right)\cos^2\alpha=\ctg^2\alpha;$

4) $\frac{\sqrt3-2\sin\alpha}{2\cos\alpha-1}=\frac{1+2\cos\alpha}{2\sin\alpha+\sqrt3};$

8) $\frac{\sin^2\alpha}{\ctg^2\alpha-\cos^2\alpha}=\tg^4.$