Question

Find the value of sin theta + cos theta by sin theta minus cos theta + sin theta minus cos theta by sin theta + cos theta

Answer 1

Solution

→ (sin∅ + cos∅)/(sin∅ - cos∅) + (sin∅ - cos∅)/(sin∅ + cos∅)

→ [(sin∅ + cos∅)² + (sin∅ - cos∅)²]/(sin∅ - cos∅)(sin∅ + cos∅)

→ [sin²∅ + cos²∅ + 2sin∅·cos∅ + sin²∅ + cos²∅ - 2sin∅·cos∅]/(sin²∅ - cos²∅)

→ 2(sin²∅ + cos²∅)/(sin²∅ - 1 + sin²∅)

→ 2/(2sin²∅ - 1)

Remember

• cos²∅ = 1 - sin²∅
• sin²∅ + cos²∅ = 1