Home > CALC > Chapter 4 > Lesson 4.5.1 > Problem4-165

4-165.

Solve for $x$. Assume $x$ is measured in radians. Hint: First use a substitution to make the problem easier.

1. $2\operatorname{ sin}^2(x + 1)-\operatorname{sin}(x + 1) − 1 = 0$

Let $U =\operatorname{sin}(x + 1)$
so $2U^2 − U − 1 = 0$

Solve for $U$, then substitute to solve for $x$.

Remember to mention ALL solutions.

2. $( x ^ { 2 } - 2 x + 1 ) - 3 \sqrt { x ^ { 2 } - 2 x + 1 } = - 2$

Let $U = x^2 − 2x + 1$