Trigonometric Functions

Concept: Use identity:
Step 1: Apply identity.
Step 2: Rewrite the integral.
Step 3:

Concept: Use the standard form: after completing the square.
Step 1: Rewrite the expression inside root.
Step 2: Complete the square.
Step 3: Use substitution. Let

Concept: We use standard derivatives:

This helps in identifying integrals directly.
Step 1: Rewrite the integrand. But a better approach is to split:
Step 2: Integrate separately.
Step 3:

Concept: Use identity:
Step 1: Find inner value.
Step 2:
Step 3:
Step 4:

Concept:
Step 1: Given angle.
Step 2:
Step 3:

Concept: Range of inverse cosine function:
Step 1: Apply definition.