Question

Simplify: (1+tan²thita) (1-sin thita) (1+sin thita)

Answer 1

Step-by-step explanation:

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Answer 2

Given

Simplify: (1+tan²thita) (1-sin thita) (1+sin thita)

Solution

→ (1 + tan²∅)(1 - sin∅)(1 + sin∅)

★ sec²∅ - tan²∅ = 1

★ a² - b² = (a + b)(a - b)

→ sec²∅[(1)² - (sin∅)²]

→ sec²∅[1 - sin²∅]

★ sin²∅ + cos²∅ = 1

→ sec²∅.cos²∅

★ 1/cos∅ = sec∅

→ 1/cos² ∅ × cos²∅

→ 1

Trigonometric identities

• sin²∅ + cos²∅ = 1

• 1 + cot²∅ = cosec²∅

• 1 + tan²∅ = sec²∅