Math Assignment Help With Trigonometric Or Conditional Identities

9.10 Trigonometric Or Conditional Identities:

1. i) If A+B+C = π

Then,

A+B = π – C, B+C = π – A , A+C = π – B

So,

Sin (A+B) = sin (π – C) = sinC

Cos (A+B) = cos (π – C) = - cosC

Tan (A+B) = tan (π – C) = - tanC

ii) If (A/2) + (B/2) + (C/2) = π/2

Then,

(A/2)+(B/2) =( π/2 – C/2), (B/2)+(C/2) =(π/2) –(A/2) , (A/2)+(C/2) =( π/2) – (B/2)

So,

Sin (A+B)/2 = sin (π/2 – C/2) = cos(C/2)

Cos (A+B)/2 = cos (π/2 – C/2) = sin (C/2)

Tan (A+B)/2 = tan (π/2 – C/2) = cot (C/2)

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