Question

Pls solve this trigo class 10 ques fast

Q1 C

Answer 1

Evaluate

cos²∅ - 3 cos∅ + 2 = 2 sin²∅

Solution

L.H.S → cos²∅ - 3cos∅ + 2

→ cos²∅ - cos∅ - 2cos∅ + 2

→ cos∅(cos∅ - 1) - 2(cos∅ - 1)

→ (cos∅ - 1)(cos∅ - 2)

R.H.S → 2 sin²∅

→ 2(1 - cos²∅)

→ 2(1 - cos∅)(1 + cos∅)

→ - 2(cos∅ - 1)(cos∅ + 1)

Since, L.H.S = R.H.S

→ (cos∅ - 1)(cos∅ - 2) = - 2(cos∅ - 1)(cos∅ + 1)

→ cos∅ - 2 = - 2(cos∅ + 1)

→ cos∅ - 2 = - 2cos∅ - 2

→ - 2 + 2 = - 2cos∅ - cos∅

→ 0 = - 3 cos∅

→ 0 = cos∅

→ cos90° = 0

Hence, cos90° = cos∅

→ ∅ = 90°

Hence value of theta is 90°.